How to find the measure of an angle - HSPT Math
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The measure of 3 angles in a triangle are in a 1:2:3 ratio. What is the measure of the middle angle?
The measure of 3 angles in a triangle are in a 1:2:3 ratio. What is the measure of the middle angle?
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The angles in a triangle sum to 180 degrees. This makes the middle angle 60 degrees.
The angles in a triangle sum to 180 degrees. This makes the middle angle 60 degrees.
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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?
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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.
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Two angles are supplementary and have a ratio of 1:4. What is the size of the smaller angle?
Two angles are supplementary and have a ratio of 1:4. What is the size of the smaller angle?
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Since the angles are supplementary, their sum is 180 degrees. Because they are in a ratio of 1:4, the following expression could be written:
x+4x=180
5x=180
$x=36^{circ}$
Since the angles are supplementary, their sum is 180 degrees. Because they are in a ratio of 1:4, the following expression could be written:
x+4x=180
5x=180
$x=36^{circ}$
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What is the sum of the interior angles of a triangle?
What is the sum of the interior angles of a triangle?
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The sum of the three interior angles of a triangle is 
degrees.
The sum of the three interior angles of a triangle is
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Two of the interior angles of a triangle measure 
and 
. What is the greatest measure of any of its exterior angles?
Two of the interior angles of a triangle measure
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The interior angles of a triangle must have measures whose sum is 
, so the measure of the third angle must be 
.
By the Triangle Exterior-Angle Theorem, an exterior angle of a triangle measures the sum of its remote interior angles; therefore, to get the greatest measure of any exterior angle, we add the two greatest interior angle measures: 
The interior angles of a triangle must have measures whose sum is
By the Triangle Exterior-Angle Theorem, an exterior angle of a triangle measures the sum of its remote interior angles; therefore, to get the greatest measure of any exterior angle, we add the two greatest interior angle measures:
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Call the three angles of a triangle 
.
The measure of 
is twenty degrees greater than that of 
; the measure of 
is thirty degrees less than twice that of 
. If 
is the measure of 
, then which of the following equations would we need to solve in order to calculate the measures of the angles?
Call the three angles of a triangle
The measure of
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The measure of 
is twenty degrees greater than the measure 
of 
, so its measure is 20 added to that of 
- that is, 
.
The measure of 
is thirty degrees less than twice that of 
. Twice the measure of 
is 
, and thirty degrees less than this is 30 subtracted from 
- that is, 
.
The sum of the measures of the three angles of a triangle is 180, so, to solve for 
- thereby allowing us to calulate all three angle measures - we add these three expressions and set the sum equal to 180. This yields the equation:
The measure of
The measure of
The sum of the measures of the three angles of a triangle is 180, so, to solve for
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Call the three angles of a triangle 
.
The measure of 
is forty degrees less than that of 
; the measure of 
is ten degrees less than twice that of 
. If 
is the measure of 
, then which of the following equations would we need to solve in order to calculate the measures of the angles?
Call the three angles of a triangle
The measure of
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The measure of 
is forty degrees less than the measure 
of 
, so its measure is 40 subtracted from that of 
- that is, 
.
The measure of 
is ten degrees less than twice that of 
. Twice the measure of 
is 
, and ten degrees less than this is 10 subtracted from 
- that is, 
.
The sum of the measures of the three angles of a triangle is 180, so, to solve for 
- thereby allowing us to calulate all three angle measures - we add these three expressions and set the sum equal to 180. This yields the equation:
The measure of
The measure of
The sum of the measures of the three angles of a triangle is 180, so, to solve for
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Two interior angles of a triangle adds up to 
degrees. What is the measure of the other angle?
Two interior angles of a triangle adds up to
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The sum of the three angles of a triangle add up to 180 degrees. Subtract 64 degrees to determine the third angle.
The sum of the three angles of a triangle add up to 180 degrees. Subtract 64 degrees to determine the third angle.
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What is 
of the measure of a right angle?
What is
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A right angle has a measure of 
. One fifth of the angle is:
A right angle has a measure of
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What angle is complementary to 
?
What angle is complementary to
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To find the other angle, subtract the given angle from 
since complementary angles add up to 
.
The complementary is:
To find the other angle, subtract the given angle from
The complementary is:
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What is the supplementary angle to 
?
What is the supplementary angle to
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Supplementary angles add up to 
. In order to find the correct angle, take the known angle and subtract that from 
.
Supplementary angles add up to
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What angle is complement to 
?
What angle is complement to
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The complement to an angle is ninety degrees subtract the angle since two angles must add up to 90. In this case, since we are given the angle in radians, we are subtracting from 
instead to find the complement. The conversion between radians and degrees is: 
Reconvert the fractions to the least common denominator.
Reduce the fraction.
The complement to an angle is ninety degrees subtract the angle since two angles must add up to 90. In this case, since we are given the angle in radians, we are subtracting from
Reconvert the fractions to the least common denominator.
Reduce the fraction.
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The above diagram shows a spinner. The radius of the smaller quarter-circles is half that of the larger quarter-circles.
A player spins the above spinner. What is the probability that the spinner will stop while pointing inside a red region?
The above diagram shows a spinner. The radius of the smaller quarter-circles is half that of the larger quarter-circles.
A player spins the above spinner. What is the probability that the spinner will stop while pointing inside a red region?
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The size of the regions does not matter here. What matters is the angle measurement, or, equivalently, what part of a circle each sector is.
The two smaller red regions each comprise one fourth of one fourth of a circle, or
circle.
The two larger red regions each comprise one third of one fourth of a circle, or
circle.
Therefore, the total angle measure comprises
of a circle.
This makes 
the correct probability.
The size of the regions does not matter here. What matters is the angle measurement, or, equivalently, what part of a circle each sector is.
The two smaller red regions each comprise one fourth of one fourth of a circle, or
The two larger red regions each comprise one third of one fourth of a circle, or
Therefore, the total angle measure comprises
of a circle.
This makes
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The above diagram shows a spinner. The radius of the smaller quarter-circles is half that of the larger quarter-circles.
A player spins the above spinner. What are the odds against the spinner landing while pointing inside one of the blue regions?
The above diagram shows a spinner. The radius of the smaller quarter-circles is half that of the larger quarter-circles.
A player spins the above spinner. What are the odds against the spinner landing while pointing inside one of the blue regions?
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The size of the regions does not matter here. What matters is the angle measurement, or, equivalently, what part of a circle each sector is.
Two of the blue sectors are each one third of one quarter-circle, and thus are
of one circle.
The other two blue sectors are each one fourth of one quarter-circle, and thus are
of one circle.
Therefore, the total angle measure comprises
of a circle. This makes the correct probability. As odds, this translates to
, or 
odds against the spinner landing in blue.
The size of the regions does not matter here. What matters is the angle measurement, or, equivalently, what part of a circle each sector is.
Two of the blue sectors are each one third of one quarter-circle, and thus are
of one circle.
The other two blue sectors are each one fourth of one quarter-circle, and thus are
of one circle.
Therefore, the total angle measure comprises
of a circle. This makes
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The above diagram shows a spinner. The radius of the smaller quarter-circles is half that of the larger quarter-circles.
A player spins the above spinner. What are the odds against the spinner landing while pointing inside the purple region?
The above diagram shows a spinner. The radius of the smaller quarter-circles is half that of the larger quarter-circles.
A player spins the above spinner. What are the odds against the spinner landing while pointing inside the purple region?
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The size of the regions does not matter here. What matters is the angle measurement, or, equivalently, what part of a circle each sector is.
The purple region is one third of one quarter of a circle, or, equvalently,
of a circle, so its central angle is 
of the total measures of the angles of the sectors. This makes 
the probability of the spinner stopping inside the purple region; this translates to
or 
odds against this occurrence.
The size of the regions does not matter here. What matters is the angle measurement, or, equivalently, what part of a circle each sector is.
The purple region is one third of one quarter of a circle, or, equvalently,
of a circle, so its central angle is
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In parallelogram 
, 
. Give the measure of 
in terms of 
.
In parallelogram
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and 
are a pair of adjacent angles of the parallelogram, and as such, they are supplementary - that is, their degree measures total 180. Therefore,
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The measures of the angles of 
are as follows:
Is this triangle acute, obtuse, right, or nonexistent?
The measures of the angles of
Is this triangle acute, obtuse, right, or nonexistent?
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The sum of the measures of the angles of a triangle is 180 degrees, so solve for 
in the equation:
All three angles measure less than 90 degrees and are therefore acute angles; that makes 
an acute triangle.
The sum of the measures of the angles of a triangle is 180 degrees, so solve for
All three angles measure less than 90 degrees and are therefore acute angles; that makes
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If you have a right triangle, what is the measure of the two of the angles if they are equal?
If you have a right triangle, what is the measure of the two of the angles if they are equal?
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The total degrees of the angles in a triangle are 
.
Since it is a right triangle, one of the three angles must be 
That leaves you with 
for the other two angles 
.
If they are equal, you just divide the remaining degrees by 
to get 
.
The total degrees of the angles in a triangle are
Since it is a right triangle, one of the three angles must be
That leaves you with
If they are equal, you just divide the remaining degrees by
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If you have a right triangle with an angle measuring 45 degrees, what is the third angle measurement?
If you have a right triangle with an angle measuring 45 degrees, what is the third angle measurement?
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A right triangle has one 90 degree angle and all three angles must equal 180 degrees.
To find the answer, just subtract the two angles you have from the total to get
The angle we have are,
.
Substituting these into the formula results in the solution.
.
A right triangle has one 90 degree angle and all three angles must equal 180 degrees.
To find the answer, just subtract the two angles you have from the total to get
The angle we have are,
Substituting these into the formula results in the solution.
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In triangle ABC, Angle A = x degrees, Angle B = 2x degrees, and Angle C = 3x+30 degrees. How many degrees is Angle B?
In triangle ABC, Angle A = x degrees, Angle B = 2x degrees, and Angle C = 3x+30 degrees. How many degrees is Angle B?
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Because the interior angles of a triangle add up to 180°, we can create an equation using the variables given in the problem: x+2x+(3x+30)=180. This simplifies to 6X+30=180. When we subtract 30 from both sides, we get 6x=150. Then, when we divide both sides by 6, we get x=25. Because Angle B=2x degrees, we multiply 25 times 2. Thus, Angle B is equal to 50°. If you got an answer of 25, you may have forgotten to multiply by 2. If you got 105, you may have found Angle C instead of Angle B.
Because the interior angles of a triangle add up to 180°, we can create an equation using the variables given in the problem: x+2x+(3x+30)=180. This simplifies to 6X+30=180. When we subtract 30 from both sides, we get 6x=150. Then, when we divide both sides by 6, we get x=25. Because Angle B=2x degrees, we multiply 25 times 2. Thus, Angle B is equal to 50°. If you got an answer of 25, you may have forgotten to multiply by 2. If you got 105, you may have found Angle C instead of Angle B.
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