Question

The middle angle in a triangle is 4 times the measure of the smallest angle. The smallest angle is the difference of the largest angle and the middle angle. Find the measures of the three angles.

Find the smallest angle, largest angle, and middle angle in degrees

Answer 1

• smallest: 18°
• largest: 90°
• middle: 72°

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.