Question

Each face of a pyramid is an isosceles triangle with a 70 degree vertex angle. What are the measures of the base angles?

Answer 1

We are given that each face of a pyramid is an isosceles triangle and that its vertex angle is 70 degrees. This problem can be exemplified in the following diagram:

Since the triangle is isosceles, its base angles are the same, and the sum of the interior angles must be equal to 180 degrees. Therefore, we have the following relationship:

`70+x+x=180`

Adding like terms, we get:

`70+2x=180`

Now we solve for "x", first by subtracting 70 on both sides:

`\begin{gathered} 70-70+2x=180-70 \\ 2x=110 \end{gathered}`

Now we divide both sides by 2

`x=(110)/(2)=55`

Therefore, the base angles of the pyramid are 55 degrees.