Question

The flag of a country contains isosceles triangle.​ (Recall that an isosceles triangle contains two angles with the same​ measure.) If the measure of the third angle of the triangle is 15​° more than the measure of either of the other two​ angles, find the measure of each angle of the triangle.​ (Recall that the sum of the measures of the angles of a triangle is​ 180°.)

Answer 1

The 3 angles are 55°, 55° and 70°

Step-by-step explanation:

Let the angles of the triangle be a, a and c since two of the angles are the same we can use the same letter to describe the relationships

Sum of all angles of a triangle = 180

a + a + c ==> 2a + c = 180 (1)

We also know c = a + 15

Substituting for c in equation (1) yields

2a + (a + 15) = 180 ==> 3a + 15 = 180 ==> a = (180-15)/3 = 165/3 55°

c = 55 + 15 = 70°

Therefore the 3 angles are 55°, 55° and 70°