the transamerica pyramid building shown in the photograph has four faces shaped like isosceles triangles. The measure of a base angle of one of these triangles is about 85. What is the approximate measure of the vertex angle of the triangle?
call the base angle b, and the vertex angle v.
b+b+v = 180
170+v=180
v = 10
To find the measure of the vertex angle of the isosceles triangle, we can use the fact that the sum of the interior angles of a triangle is always 180 degrees.
An isosceles triangle has two congruent base angles (the angles opposite the congruent sides) and one vertex angle (the angle formed by the two congruent sides). Let's assume the measure of each base angle is x degrees.
Since the triangle has four faces shaped like isosceles triangles, each base angle of the triangle is about 85 degrees.
To find the measure of the vertex angle, we subtract two times the base angle from 180 degrees:
Vertex angle = 180 degrees - (2 * base angle)
Vertex angle = 180 degrees - (2 * 85 degrees)
Vertex angle ≈ 180 degrees - 170 degrees
Vertex angle ≈ 10 degrees
Therefore, the approximate measure of the vertex angle of the isosceles triangle is about 10 degrees.