The measures of the angles of a triangle are in the extended ratio 2: 2: 8. What is the measure of the smallest angle?

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

Answer: For the angles of a triangle given in the ratio 2: 2: 8, the measure of the smallest angle of the triangle is 30º.

Let us find the smallest angle of this triangle.

Explanation:

Given that the angles of a triangle are in the ratio of 2: 2: 8.

Let the angles be 2x,  2x, and 8x.

By angle sum property of triangle,

⇒ 2 x + 2 x + 8x = 180º

⇒ 12 x =  180º

⇒ x =  180º / 12

⇒ x =  15º

The measures of the angles are:

2x  = 2 × 15º = 30º

2x  = 2 × 15º = 30º

8x = 8 × 15º = 120º

Thus, the measure of the smallest angle of the triangle is 30º.