All ACT Math Resources
Example Question #1 : Acute / Obtuse Triangles
Two interior angles in an obtuse triangle measure and . What is the measurement of the third angle.
Interior angles of a triangle always add up to 180 degrees.
Example Question #2 : How To Find The Measure Of An 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 , 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:
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.
Example Question #3 : Acute / Obtuse Triangles
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°)
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°
Example Question #4 : Acute / Obtuse Triangles
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°.
Example Question #2 : How To Find An Angle In An Acute / Obtuse Triangle
Points A, B, and C are collinear (they lie along the same line). The measure of angle CAD is . The measure of angle CBD is . The length of segment is 4.
Find the measure of .
The measure of is . Since , , and are collinear, and the measure of is , we know that the measure of is .
Because the measures of the three angles in a triangle must add up to , and two of the angles in triangle are and , the third angle, , is .