Question

each face of a pyramid is an isosceles triangle with a 64° vertex angle. what are the measures of the base angles?the measures of the base angles are ......°

Answer 1

An isosceles triangle has two equal angles and one different angle. The angle that is different is called the vertex angle.

We can see in the following image a representation of this problem:

The vertex angle is at the top, the two angles marked in yellow have to be equal because it is an isosceles triangle.

The vertex angle is 64° and we will call the yellow angles x:

Now, we use the following property of triangles:

• The sum of all of the angles inside a triangle is 180°

So we need to add the angles in the triangle of this problem and equal them to 180°:

`x+x+64=180`

Now we solve this equation for x. First, we add the like terms:

`2x+64=180`

Now, subtract 64 to both sides:

`\begin{gathered} 2x=180-64 \\ 2x=116 \end{gathered}`

Next, divide both sides by 2:

`\begin{gathered} x=(116)/(2) \\ x=58 \end{gathered}`

The value of x is 58°. (x represents the base angles).

Answer: The measures of the base angles are 58°