geodesic dome and isosceles triangle

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

58.5​°

more than the measure of either of the two equal angles. Find the measure of the three angles.

Answer 1

Let's denote the measure of each of the two equal angles of the isosceles triangle as x.

Given that the third angle is 58.5 degrees more than the measure of either of the two equal angles, the measure of the third angle is x + 58.5 degrees.

In a triangle, the sum of the angles is always 180 degrees. Therefore, we can set up the following equation:

x + x + (x + 58.5 degrees) = 180 degrees

Simplify and combine like terms:

3x + 58.5 degrees = 180 degrees

Next, solve for x:

3x = 180 degrees - 58.5 degrees

3x = 121.5 degrees

x = 121.5 degrees / 3

x = 40.5 degrees

Thus, the measure of each of the two equal angles is 40.5 degrees.

The measure of the third angle is:

x + 58.5 degrees = 40.5 degrees + 58.5 degrees = 99 degrees

Therefore, the measures of the three angles in the isosceles triangle are:

40.5 degrees, 40.5 degrees, and 99 degrees