Question

The flag of a country contains an 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 40​° more than three times 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

Let us start with the unknown. Let us give one of the base angles the value of x. The other base angle is also x since both the base angles in an isosceles triangle will be equal. The remaining angle is 40 more than three times one of the base angles.It is 3x + 40. Here we get the equation

x+x+3x+40=180

5x + 40 = 180

5x = 180 - 40 = 140

Therefore x = 140/5 = 28

So the angles are 28, 28 and 124.

The third angle is 3 times 28 + 40 = 84 + 40 = 124.