Question

Measures of the angles of a triangle are in the extended ratio 4:12:14. What is the measure of the smallest angle

A. 6°
B. 24°
C. 72°
D. 84°

Answer 1

24°

Explanation:

The sum of the ratios is 30. We know that the degree measure of a triangle is 180, so if we divide 180 by 3 we get increments of 6°. That means that 4 parts algebraically can be expressed as 4(6°); 12 parts as 12(6°); 14 parts as 14(6°). That gives us angles of 24°, 72°, 84°. If we add those up we do indeed get 180°, so the smallest angle measure in that extended ratio is 24°