Answer:
- smallest: 18°
- largest: 90°
- middle: 72°
Step-by-step explanation:
We can solve this using the relationship between the angles together with the angle sum theorem. Let s represent the measure of the smallest angle. Then the middle angle is 4s, and the largest angle is (4s +s). The angle sum theorem tells us the sum of angles in a triangle is 180°.
smallest + middle + largest = 180°
s +(4s) +(4s +s) = 180°
10s = 180° . . . . . . . . . . . simplify
s = 18° . . . . . . . . . divide by 10
4s = 72° . . . . . . find the middle angle
4s +s = 72° +18° = 90° . . . . . find the largest angle
The smallest, largest, and middle angles are 18°, 90°, and 72°, respectively.
