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 twice 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: Let the measure of each of the equal - angled pair be $x$.

The third angle's measure is $2x + 30$.

Step2: Use the angle - sum property of a triangle.

The sum of the interior angles of a triangle is $180^{\circ}$, so $x+x+(2x + 30)=180$.

Step3: Simplify the left - hand side of the equation.

Combining like terms, we get $4x+30 = 180$.

Step4: Solve for $x$.

Subtract 30 from both sides: $4x=180 - 30=150$. Then divide both sides by 4: $x=\frac{150}{4}=37.5$.

Step5: Find the measure of the third angle.

Substitute $x = 37.5$ into the expression for the third angle: $2x+30=2\times37.5 + 30=75 + 30=105$.

Answer:

The first angle is $37.5^{\circ}$, the second angle is $37.5^{\circ}$, and the third angle is $105^{\circ}$