The measures of the angles in a triangle are in the extended ratio 3 : 4 : 8. What are the measures of the angles?

A triangle is a polygon with three sides, three angles, and three vertices. The sum of interior angles of a triangle is 180º.

Answer: The measures of angles are 36º, 48º and 96º.

Let us find the angles to this triangle.

Explanation:

Given that the angles in the triangle are in the ratio of 3 : 4 : 8.

Let the triangle be named as ABC and its angles be 3x, 4x and 8x.

By angle sum property of triangle,

⇒ 3x + 4x + 8x = 180º

⇒ 15x =  180º

⇒ x =  180º / 15

⇒ x =  12º

The measures of angles are:

• 3x = 3 × 12º = 36º
• 4x = 4 × 12º = 48º
• 8x = 8 × 12º = 96º

Thus, the measures of angles are 36º, 48º and 96º.