Question

The diagram shows a triangular face of the Pyramid of Cestius in Rome, Italy. The length of the base of the triangle is 30 meters.

The lengths of the other two sides of the triangle are both 36 meters.
b. The measure of <3 is 40°. What are the measures of <1 and <2?
Explain your reasoning.

Answer 1

a. The particular triangle is an isosceles triangle (two sides are equal in length)

b. The measure of <1 and <2 is 70° each.

How to determine angle of a triangle

In this triangle from the Pyramid of Cestius, you're given the lengths of the sides and one angle, <3.

Given:

Length of the base = 30 meters

Length of the other two sides = 36 meters each

<3 = 40°

To find <1 and <2, you use the fact that the sum of angles in a triangle is 180 degrees.

This particular triangle is an isosceles triangle (two sides are equal in length), and <1 and <2 are the angles adjacent to the base.

In an isosceles triangle, the base angles are congruent.

So, <1 and <2 are equal.

Let x be the measure of <1 and <2.

<1 + <2 + <3 = 180°

x + x + 40° = 180°

2x + 40° = 180°

2x = 180° - 40°

2x = 140°

x = 140° / 2

x = 70°

Therefore, <1 = <2 = 70° each.