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 15° more than 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 the equal - angled pair be $x$ degrees.

The third angle is $x + 15$ degrees.

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

The sum of the interior angles of a triangle is $180^{\circ}$. So, $x+x+(x + 15)=180$.

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

Combining like terms, we get $3x+15 = 180$.

Step4: Isolate the variable term.

Subtract 15 from both sides: $3x=180 - 15=165$.

Step5: Solve for $x$.

Divide both sides by 3: $x=\frac{165}{3}=55$.

Step6: Find the measure of the third angle.

The third angle is $x + 15$, so it is $55+15 = 70$.

Answer:

The first angle is $55^{\circ}$, the second angle is $55^{\circ}$, and the third angle is $70^{\circ}$.