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°.)
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.
