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 45° 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 two equal - angled sides be $x$ degrees.

Let the measure of the third angle be $y$ degrees. We know that $y=x + 45$.

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

The sum of the interior angles of a triangle is $180^{\circ}$. So, $x+x + y=180$. Substitute $y=x + 45$ into the equation: $x+x+(x + 45)=180$.

Step3: Simplify the equation.

Combine like terms: $3x+45 = 180$.

Step4: Solve for $x$.

Subtract 45 from both sides: $3x=180 - 45=135$. Then divide both sides by 3: $x = 45$.

Step5: Solve for $y$.

Since $y=x + 45$, then $y=45 + 45=90$.

Answer:

The first angle is $45^{\circ}$, the second angle is $45^{\circ}$, and the third angle is $90^{\circ}$.