The measures of the angles of a triangle are in the extended ratio 3 : 5 : 7. What is the measure of the smallest angle?

a. 12°
b. 36°
c. 60°
d. 84°

1 answer

The sum of the angles in a triangle is always 180 degrees. Let x be the common factor that multiplies the ratios 3, 5, and 7. Then, the angles can be expressed as 3x, 5x, and 7x.

The sum of these angles is:

3x + 5x + 7x = 15x

Since the sum of the angles in a triangle is 180 degrees, we can set up the equation:

15x = 180

Solving for x, we get:

x = 12

Therefore, the angles are:

3x = 36 degrees
5x = 60 degrees
7x = 84 degrees

The smallest angle is 36 degrees, so the answer is (b) 36°.