Finding the measure of angle 2

Hello! Today we are going to find the measure of angle two in this geometric diagram. Let's start by breaking the figure down into several triangles.

First, let's look at the triangle on the far left. Notice the two tick marks on its sides? This indicates that it is an isosceles triangle.

Because it is an isosceles triangle, the base angles are equal. Let's call them x. The sum of the angles in a triangle is one hundred and eighty degrees.

Simplified, that is forty-eight plus two x equals one hundred and eighty.

Subtracting forty-eight from both sides, we get two x equals one hundred and thirty-two.

Dividing by two, we find that each base angle is sixty-six degrees.

Now, look at angle one. It is vertically opposite to one of the base angles we just found. Vertical angles are equal, so angle one must also be sixty-six degrees.