Question

A geodesic dome is compromised 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 85.5 degrees more than the measure of the two equal angles. Find the measure of the three angles.

Answer 1

The measure of the third angle is 117 degrees and the measure of the two equal angles is 31.5 degrees

Explanation:

The correct question is

A geodesic dome is compromised 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 85.5 degrees more than the measure of either of the two equal angles. Find the measure of the three angles

we know that

An isosceles triangle has two sides and two equal interior angles

Let

x -----> the measure of the third angle

y ----> the measure of either of the two equal angles

we know that

`x+2y=180\°` -----> equation A

`x=85.5\°+y` -----> equation B

substitute equation B in equation A and solve for y

`85.5\°+y+2y=180\°`

`3y=180\°-85.5\°`

`3y=94.5\°`

`y=31.5\°`

`x=85.5\°+31.5\°=117\°`

therefore

The measure of the third angle is 117 degrees and the measure of either of the two equal angles is 31.5 degrees