Problema Solution
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 85.5 degrees more than the measure of either of the two equal angles. Find the measure of the three angles.
Answer provided by our tutors
Let x and y represent the angles of the isosceles triangle
2x + y = 180 (the sum of the angles in a triangle is 180 degrees)
The measure of the third angle is 85.5 degrees more than the measure of either of the two equal angles:
y = x + 85.5
By solving the system of equations:
2x + y = 180
y = x + 85.5
........
........
x = 31.5 degrees
y = 117 degrees
The measure of the three angles in the isosceles triangle are: 31.5 degrees and 117 degrees.