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

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

Answer 1

triangle? sum of angles is 180

70.5+x+2x=180
3x=109.5
x=36.5

Answer 2

Let's represent the equal angles in the isosceles triangle as x degrees each.

According to the given information, the measure of the third angle is 70.5 degrees more than each of the equal angles. Therefore, the measure of the third angle is x + 70.5 degrees.
The sum of the angles in a triangle is always 180 degrees.
We can set up the equation:
x + x + x + 70.5 = 180
Combining like terms,
3x + 70.5 = 180
Subtracting 70.5 from both sides,
3x = 180 - 70.5
3x = 109.5
Dividing both sides by 3,
x = 109.5 / 3
x ≈ 36.5
Therefore, each equal angle in the isosceles triangle measures approximately 36.5 degrees.
The third angle measures x + 70.5 = 36.5 + 70.5 = 107 degrees.
So, the three angles in the triangle are approximately 36.5 degrees, 36.5 degrees, and 107 degrees.

Answer 3

To find the measure of the three angles of an isosceles triangle in the geodesic dome, we need to use the information given in the problem.

Let's assume that the measure of each of the two equal angles in the isosceles triangle is x degrees. According to the problem, the measure of the third angle is 70.5 degrees more than each of the two equal angles. Therefore, the measure of the third angle would be x + 70.5 degrees.

Since the sum of the angles in any triangle is always 180 degrees, we can write the equation:

x + x + (x + 70.5) = 180

Simplifying the equation, we have:

3x + 70.5 = 180

Subtracting 70.5 from both sides, we get:

3x = 109.5

Dividing both sides by 3, we find:

x = 36.5

So the measure of each of the two equal angles in the isosceles triangle is 36.5 degrees.

Now, let's find the measure of the third angle:

x + 70.5 = 36.5 + 70.5 = 107

Therefore, the three angles in the isosceles triangle are 36.5 degrees, 36.5 degrees, and 107 degrees.