### Video Transcript

What is the measure of angle ππΉπ?

The first thing we want to do is identify angle ππΉπ. Angles can be named by three points. This one is named ππΉπ and that means this is the angle weβre interested in. We want to measure this space. To do that, weβll have to remember some rules about intersecting lines.

One of the rules weβll need to remember is that when two lines intersect, opposite angles have the same measure. And we call those opposite congruent angles βverticals angles.β Hereβs an example: angle π΄πΆπ΅ is an opposite angle to angle πΉπΆπ. So angle πΉπΆπ is equal. It has the same measure as angle π΄πΆπ΅. These two angles are vertical angles. We can label angle ππΆπΉ as 32 degrees.

Another rule that can help us here is the fact that the sum of the interior angles in a triangle measure 180 degrees. Inside this figure, we have a triangle β πΆπΉπ. And if we add up all the angles inside this triangle, they will equal 180 degrees. We have 32 degrees. This symbol represents a right angle. And right angles measure 90 degrees plus our unknown measure of angle ππΉπΆ is equal to 180 degrees.

We can add our first two angles together: 32 plus 90 equals 122 degrees. 122 degrees plus our missing angle has to equal 180 degrees. If we take 180 degrees and subtract the 122 degrees, we come up with 58 degrees. Angle ππΉπΆ has a measure of 58 degrees.

But we are still looking for the measure of angle ππΉπ, here in pink. To find that, weβll go back to the first rule we started with. We need to go back to what we know about vertical angles. When two lines intersect, opposite angles have the same measure. Our unknown angle ππΉπ is a vertical angle of ππΉπΆ. Angle ππΉπ must be equal to a measure of 58 degrees.

Angle ππΉπ equals 58 degrees.