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 □°.

Explanation:

Step1: Set up the equation

Let the measure of each of the two equal angles be \(x\). Then the measure of the third angle is \(3x + 30\).
Since the sum of angles in a triangle is \(180^{\circ}\), we have the equation \(x+x+(3x + 30)=180\).

Step2: Simplify the equation

Combine like - terms: \(5x+30 = 180\).
Subtract 30 from both sides: \(5x=180 - 30\), so \(5x=150\).

Step3: Solve for \(x\)

Divide both sides by 5: \(x=\frac{150}{5}=30\).

Step4: Find the measure of the third angle

Substitute \(x = 30\) into \(3x + 30\). We get \(3\times30+30=90 + 30=120\).

Answer:

The first angle is \(30^{\circ}\), the second angle is \(30^{\circ}\), and the third angle is \(120^{\circ}\).