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 30° 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°)

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 30° 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°)

The first angle is
the second angle is
, and the third angle is

Answer 1

Let's call the measure of each of the other two angles x.

According to the given information, the third angle is 30° more than three times the measure of either of the other two angles. Thus, the measure of the third angle is 3x + 30°.

We know that the sum of the measures of the angles of a triangle is 180°. Therefore, we can set up the following equation:

x + x + (3x + 30°) = 180°

Combining like terms, we get:

5x + 30° = 180°

Subtracting 30° from both sides, we have:

5x = 150°

Dividing both sides by 5, we get:

x = 30°

Therefore, the first angle is 30°, the second angle is 30°, and the third angle is 3(30°) + 30° = 120°.

So, the measure of each angle of the triangle is:

First angle: 30°
Second angle: 30°
Third angle: 120°