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 25° 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 (square^{circ}), the second angle is (square^{circ}), and the third angle is (square^{circ}).

Explanation:

Step1: Let the measure of the first - two equal angles be $x$.

The third angle is $x + 25$.

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

The sum of the interior angles of a triangle is $180^{\circ}$, so $x+x+(x + 25)=180$.

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

Combining like terms, we get $3x+25 = 180$.

Step4: Solve for $x$.

Subtract 25 from both sides: $3x=180 - 25=155$. Then $x=\frac{155}{3}\approx51.67^{\circ}$.
The third angle is $x + 25=\frac{155}{3}+25=\frac{155 + 75}{3}=\frac{230}{3}\approx76.67^{\circ}$.

Answer:

The first angle is $\frac{155}{3}\approx51.67^{\circ}$, the second angle is $\frac{155}{3}\approx51.67^{\circ}$, and the third angle is $\frac{230}{3}\approx76.67^{\circ}$