Question

a geodesic dome is composed of two different types of triangular panels. one of these is an isosceles triangle. in one geodesic dome, the measure of the third angle is 73.5° more than the measure of either of the two equal angles. find the measure of the three angles. the measure of each equal angle is . the measure of the third angle is .

Explanation:

Step1: Let the measure of each equal - angle be $x$.

The measure of the third angle is $x + 73.5^{\circ}$.

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

The sum of the interior angles of a triangle is $180^{\circ}$. So, $x+x+(x + 73.5^{\circ})=180^{\circ}$.

Step3: Combine like terms.

$3x+73.5^{\circ}=180^{\circ}$.

Step4: Solve for $x$.

Subtract $73.5^{\circ}$ from both sides: $3x=180^{\circ}-73.5^{\circ}=106.5^{\circ}$. Then $x=\frac{106.5^{\circ}}{3}=35.5^{\circ}$.
The measure of the third angle is $x + 73.5^{\circ}=35.5^{\circ}+73.5^{\circ}=109^{\circ}$.

Answer:

The measure of each equal angle is $35.5^{\circ}$. The measure of the third angle is $109^{\circ}$.