Question

An animal pen is in the shape of a triangle. One of the interior angles of the triangle is 60°. The measures of the other interior angles are in the ratio 1 ∶ 7. What are the measures of the other interior angles?

Answer 1

The measures of the other interior angles are 15° and 105°

Explanation:

The given parameter of the measures of the interior angles of the triangle are;

The measure of one of the interior angle of the triangle = 60°

The ratio of the measure of the other interior angles = 1 : 7

Let the x represent one of the other interior angles and y represent the third interior angle, we have;

x + y = 180 - 60 = 120

x : y = 1 : 7

x = 1 part of 8 parts of 120°

y = 7 parts of 8 parts of 120°

Therefore;

x = 1/(1 + 7) × 120 = 1/8 × 120° = 15°

x = 15°

y = 7/(1 + 7) = 7/8 × 120° = 105°

y = 105°

The measures of the other interior angles are 15° and 105°.