How to find an angle in an acute / obtuse triangle - ACT Math
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In the triangle below, AB=BC (figure is not to scale) . If angle A is 41°, what is the measure of angle B?
A (Angle A = 41°)
B C
In the triangle below, AB=BC (figure is not to scale) . If angle A is 41°, what is the measure of angle B?
A (Angle A = 41°)
B C
If angle A is 41°, then angle C must also be 41°, since AB=BC. So, the sum of these 2 angles is:
41° + 41° = 82°
Since the sum of the angles in a triangle is 180°, you can find out the measure of the remaining angle by subtracting 82 from 180:
180° - 82° = 98°
If angle A is 41°, then angle C must also be 41°, since AB=BC. So, the sum of these 2 angles is:
41° + 41° = 82°
Since the sum of the angles in a triangle is 180°, you can find out the measure of the remaining angle by subtracting 82 from 180:
180° - 82° = 98°
Compare your answer with the correct one above
Points A, B, C, D are collinear. The measure of ∠ DCE is 130° and of ∠ AEC is 80°. Find the measure of ∠ EAD.
Points A, B, C, D are collinear. The measure of ∠ DCE is 130° and of ∠ AEC is 80°. Find the measure of ∠ EAD.
To solve this question, you need to remember that the sum of the angles in a triangle is 180°. You also need to remember supplementary angles. If you know what ∠ DCE is, you also know what ∠ ECA is. Hence you know two angles of the triangle, 180°-80°-50°= 50°.
To solve this question, you need to remember that the sum of the angles in a triangle is 180°. You also need to remember supplementary angles. If you know what ∠ DCE is, you also know what ∠ ECA is. Hence you know two angles of the triangle, 180°-80°-50°= 50°.
Compare your answer with the correct one above
Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is $30^{circ}$. The measure of angle CBD is $60^{circ}$. The length of segment $\overline{AD}$ is 4.
Find the measure of angle ADB.
Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is $30^{circ}$. The measure of angle CBD is $60^{circ}$. The length of segment $\overline{AD}$ is 4.
Find the measure of angle ADB.
The measure of angle ADB is $30^{circ}$. Since A, B, and C are collinear, and the measure of angle CBD is $60^{circ}$, we know that the measure of angle ABD is $120^{circ}$.
Because the measures of the three angles in a triangle must add up to $180^{circ}$, and two of the angles in triangle ABD are $30^{circ}$ and $120^{circ}$, the third angle, angle ADB, is $30^{circ}$.
The measure of angle ADB is $30^{circ}$. Since A, B, and C are collinear, and the measure of angle CBD is $60^{circ}$, we know that the measure of angle ABD is $120^{circ}$.
Because the measures of the three angles in a triangle must add up to $180^{circ}$, and two of the angles in triangle ABD are $30^{circ}$ and $120^{circ}$, the third angle, angle ADB, is $30^{circ}$.
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Two interior angles in an obtuse triangle measure $123^{circ}$ and $11^{circ}$. What is the measurement of the third angle.
Two interior angles in an obtuse triangle measure $123^{circ}$ and $11^{circ}$. What is the measurement of the third angle.
Interior angles of a triangle always add up to 180 degrees.
Interior angles of a triangle always add up to 180 degrees.
Compare your answer with the correct one above
In a given triangle, the angles are in a ratio of 1:3:5. What size is the middle angle?
In a given triangle, the angles are in a ratio of 1:3:5. What size is the middle angle?
Since the sum of the angles of a triangle is $180^{circ}$, and given that the angles are in a ratio of 1:3:5, let the measure of the smallest angle be 
, then the following expression could be written:
x+3x+5x=180
9x=180
x=20
If the smallest angle is 20 degrees, then given that the middle angle is in ratio of 1:3, the middle angle would be 3 times as large, or 60 degrees.
Since the sum of the angles of a triangle is $180^{circ}$, and given that the angles are in a ratio of 1:3:5, let the measure of the smallest angle be
x+3x+5x=180
9x=180
x=20
If the smallest angle is 20 degrees, then given that the middle angle is in ratio of 1:3, the middle angle would be 3 times as large, or 60 degrees.
Compare your answer with the correct one above
In the triangle below, AB=BC (figure is not to scale) . If angle A is 41°, what is the measure of angle B?
A (Angle A = 41°)
B C
In the triangle below, AB=BC (figure is not to scale) . If angle A is 41°, what is the measure of angle B?
A (Angle A = 41°)
B C
If angle A is 41°, then angle C must also be 41°, since AB=BC. So, the sum of these 2 angles is:
41° + 41° = 82°
Since the sum of the angles in a triangle is 180°, you can find out the measure of the remaining angle by subtracting 82 from 180:
180° - 82° = 98°
If angle A is 41°, then angle C must also be 41°, since AB=BC. So, the sum of these 2 angles is:
41° + 41° = 82°
Since the sum of the angles in a triangle is 180°, you can find out the measure of the remaining angle by subtracting 82 from 180:
180° - 82° = 98°
Compare your answer with the correct one above
Points A, B, C, D are collinear. The measure of ∠ DCE is 130° and of ∠ AEC is 80°. Find the measure of ∠ EAD.
Points A, B, C, D are collinear. The measure of ∠ DCE is 130° and of ∠ AEC is 80°. Find the measure of ∠ EAD.
To solve this question, you need to remember that the sum of the angles in a triangle is 180°. You also need to remember supplementary angles. If you know what ∠ DCE is, you also know what ∠ ECA is. Hence you know two angles of the triangle, 180°-80°-50°= 50°.
To solve this question, you need to remember that the sum of the angles in a triangle is 180°. You also need to remember supplementary angles. If you know what ∠ DCE is, you also know what ∠ ECA is. Hence you know two angles of the triangle, 180°-80°-50°= 50°.
Compare your answer with the correct one above
Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is $30^{circ}$. The measure of angle CBD is $60^{circ}$. The length of segment $\overline{AD}$ is 4.
Find the measure of angle ADB.
Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is $30^{circ}$. The measure of angle CBD is $60^{circ}$. The length of segment $\overline{AD}$ is 4.
Find the measure of angle ADB.
The measure of angle ADB is $30^{circ}$. Since A, B, and C are collinear, and the measure of angle CBD is $60^{circ}$, we know that the measure of angle ABD is $120^{circ}$.
Because the measures of the three angles in a triangle must add up to $180^{circ}$, and two of the angles in triangle ABD are $30^{circ}$ and $120^{circ}$, the third angle, angle ADB, is $30^{circ}$.
The measure of angle ADB is $30^{circ}$. Since A, B, and C are collinear, and the measure of angle CBD is $60^{circ}$, we know that the measure of angle ABD is $120^{circ}$.
Because the measures of the three angles in a triangle must add up to $180^{circ}$, and two of the angles in triangle ABD are $30^{circ}$ and $120^{circ}$, the third angle, angle ADB, is $30^{circ}$.
Compare your answer with the correct one above
Two interior angles in an obtuse triangle measure $123^{circ}$ and $11^{circ}$. What is the measurement of the third angle.
Two interior angles in an obtuse triangle measure $123^{circ}$ and $11^{circ}$. What is the measurement of the third angle.
Interior angles of a triangle always add up to 180 degrees.
Interior angles of a triangle always add up to 180 degrees.
Compare your answer with the correct one above
In a given triangle, the angles are in a ratio of 1:3:5. What size is the middle angle?
In a given triangle, the angles are in a ratio of 1:3:5. What size is the middle angle?
Since the sum of the angles of a triangle is $180^{circ}$, and given that the angles are in a ratio of 1:3:5, let the measure of the smallest angle be , then the following expression could be written:
x+3x+5x=180
9x=180
x=20
If the smallest angle is 20 degrees, then given that the middle angle is in ratio of 1:3, the middle angle would be 3 times as large, or 60 degrees.
Since the sum of the angles of a triangle is $180^{circ}$, and given that the angles are in a ratio of 1:3:5, let the measure of the smallest angle be
x+3x+5x=180
9x=180
x=20
If the smallest angle is 20 degrees, then given that the middle angle is in ratio of 1:3, the middle angle would be 3 times as large, or 60 degrees.
Compare your answer with the correct one above
In the triangle below, AB=BC (figure is not to scale) . If angle A is 41°, what is the measure of angle B?
A (Angle A = 41°)
B C
In the triangle below, AB=BC (figure is not to scale) . If angle A is 41°, what is the measure of angle B?
A (Angle A = 41°)
B C
If angle A is 41°, then angle C must also be 41°, since AB=BC. So, the sum of these 2 angles is:
41° + 41° = 82°
Since the sum of the angles in a triangle is 180°, you can find out the measure of the remaining angle by subtracting 82 from 180:
180° - 82° = 98°
If angle A is 41°, then angle C must also be 41°, since AB=BC. So, the sum of these 2 angles is:
41° + 41° = 82°
Since the sum of the angles in a triangle is 180°, you can find out the measure of the remaining angle by subtracting 82 from 180:
180° - 82° = 98°
Compare your answer with the correct one above
Points A, B, C, D are collinear. The measure of ∠ DCE is 130° and of ∠ AEC is 80°. Find the measure of ∠ EAD.
Points A, B, C, D are collinear. The measure of ∠ DCE is 130° and of ∠ AEC is 80°. Find the measure of ∠ EAD.
To solve this question, you need to remember that the sum of the angles in a triangle is 180°. You also need to remember supplementary angles. If you know what ∠ DCE is, you also know what ∠ ECA is. Hence you know two angles of the triangle, 180°-80°-50°= 50°.
To solve this question, you need to remember that the sum of the angles in a triangle is 180°. You also need to remember supplementary angles. If you know what ∠ DCE is, you also know what ∠ ECA is. Hence you know two angles of the triangle, 180°-80°-50°= 50°.
Compare your answer with the correct one above
Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is $30^{circ}$. The measure of angle CBD is $60^{circ}$. The length of segment $\overline{AD}$ is 4.
Find the measure of angle ADB.
Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is $30^{circ}$. The measure of angle CBD is $60^{circ}$. The length of segment $\overline{AD}$ is 4.
Find the measure of angle ADB.
The measure of angle ADB is $30^{circ}$. Since A, B, and C are collinear, and the measure of angle CBD is $60^{circ}$, we know that the measure of angle ABD is $120^{circ}$.
Because the measures of the three angles in a triangle must add up to $180^{circ}$, and two of the angles in triangle ABD are $30^{circ}$ and $120^{circ}$, the third angle, angle ADB, is $30^{circ}$.
The measure of angle ADB is $30^{circ}$. Since A, B, and C are collinear, and the measure of angle CBD is $60^{circ}$, we know that the measure of angle ABD is $120^{circ}$.
Because the measures of the three angles in a triangle must add up to $180^{circ}$, and two of the angles in triangle ABD are $30^{circ}$ and $120^{circ}$, the third angle, angle ADB, is $30^{circ}$.
Compare your answer with the correct one above
Two interior angles in an obtuse triangle measure $123^{circ}$ and $11^{circ}$. What is the measurement of the third angle.
Two interior angles in an obtuse triangle measure $123^{circ}$ and $11^{circ}$. What is the measurement of the third angle.
Interior angles of a triangle always add up to 180 degrees.
Interior angles of a triangle always add up to 180 degrees.
Compare your answer with the correct one above
In a given triangle, the angles are in a ratio of 1:3:5. What size is the middle angle?
In a given triangle, the angles are in a ratio of 1:3:5. What size is the middle angle?
Since the sum of the angles of a triangle is $180^{circ}$, and given that the angles are in a ratio of 1:3:5, let the measure of the smallest angle be , then the following expression could be written:
x+3x+5x=180
9x=180
x=20
If the smallest angle is 20 degrees, then given that the middle angle is in ratio of 1:3, the middle angle would be 3 times as large, or 60 degrees.
Since the sum of the angles of a triangle is $180^{circ}$, and given that the angles are in a ratio of 1:3:5, let the measure of the smallest angle be
x+3x+5x=180
9x=180
x=20
If the smallest angle is 20 degrees, then given that the middle angle is in ratio of 1:3, the middle angle would be 3 times as large, or 60 degrees.
Compare your answer with the correct one above
In the triangle below, AB=BC (figure is not to scale) . If angle A is 41°, what is the measure of angle B?
A (Angle A = 41°)
B C
In the triangle below, AB=BC (figure is not to scale) . If angle A is 41°, what is the measure of angle B?
A (Angle A = 41°)
B C
If angle A is 41°, then angle C must also be 41°, since AB=BC. So, the sum of these 2 angles is:
41° + 41° = 82°
Since the sum of the angles in a triangle is 180°, you can find out the measure of the remaining angle by subtracting 82 from 180:
180° - 82° = 98°
If angle A is 41°, then angle C must also be 41°, since AB=BC. So, the sum of these 2 angles is:
41° + 41° = 82°
Since the sum of the angles in a triangle is 180°, you can find out the measure of the remaining angle by subtracting 82 from 180:
180° - 82° = 98°
Compare your answer with the correct one above
Points A, B, C, D are collinear. The measure of ∠ DCE is 130° and of ∠ AEC is 80°. Find the measure of ∠ EAD.
Points A, B, C, D are collinear. The measure of ∠ DCE is 130° and of ∠ AEC is 80°. Find the measure of ∠ EAD.
To solve this question, you need to remember that the sum of the angles in a triangle is 180°. You also need to remember supplementary angles. If you know what ∠ DCE is, you also know what ∠ ECA is. Hence you know two angles of the triangle, 180°-80°-50°= 50°.
To solve this question, you need to remember that the sum of the angles in a triangle is 180°. You also need to remember supplementary angles. If you know what ∠ DCE is, you also know what ∠ ECA is. Hence you know two angles of the triangle, 180°-80°-50°= 50°.
Compare your answer with the correct one above
Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is $30^{circ}$. The measure of angle CBD is $60^{circ}$. The length of segment $\overline{AD}$ is 4.
Find the measure of angle ADB.
Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is $30^{circ}$. The measure of angle CBD is $60^{circ}$. The length of segment $\overline{AD}$ is 4.
Find the measure of angle ADB.
The measure of angle ADB is $30^{circ}$. Since A, B, and C are collinear, and the measure of angle CBD is $60^{circ}$, we know that the measure of angle ABD is $120^{circ}$.
Because the measures of the three angles in a triangle must add up to $180^{circ}$, and two of the angles in triangle ABD are $30^{circ}$ and $120^{circ}$, the third angle, angle ADB, is $30^{circ}$.
The measure of angle ADB is $30^{circ}$. Since A, B, and C are collinear, and the measure of angle CBD is $60^{circ}$, we know that the measure of angle ABD is $120^{circ}$.
Because the measures of the three angles in a triangle must add up to $180^{circ}$, and two of the angles in triangle ABD are $30^{circ}$ and $120^{circ}$, the third angle, angle ADB, is $30^{circ}$.
Compare your answer with the correct one above
Two interior angles in an obtuse triangle measure $123^{circ}$ and $11^{circ}$. What is the measurement of the third angle.
Two interior angles in an obtuse triangle measure $123^{circ}$ and $11^{circ}$. What is the measurement of the third angle.
Interior angles of a triangle always add up to 180 degrees.
Interior angles of a triangle always add up to 180 degrees.
Compare your answer with the correct one above
In a given triangle, the angles are in a ratio of 1:3:5. What size is the middle angle?
In a given triangle, the angles are in a ratio of 1:3:5. What size is the middle angle?
Since the sum of the angles of a triangle is $180^{circ}$, and given that the angles are in a ratio of 1:3:5, let the measure of the smallest angle be , then the following expression could be written:
x+3x+5x=180
9x=180
x=20
If the smallest angle is 20 degrees, then given that the middle angle is in ratio of 1:3, the middle angle would be 3 times as large, or 60 degrees.
Since the sum of the angles of a triangle is $180^{circ}$, and given that the angles are in a ratio of 1:3:5, let the measure of the smallest angle be
x+3x+5x=180
9x=180
x=20
If the smallest angle is 20 degrees, then given that the middle angle is in ratio of 1:3, the middle angle would be 3 times as large, or 60 degrees.
Compare your answer with the correct one above