### Video Transcript

Given the π΄π΅πΆπ·πΈ is a regular pentagon, find the measure of angle π΄π΅π.

Firstly, letβs mark the angle that weβre looking to find on the diagram. π΄π΅π is the angle formed when you travel from π΄ to π΅ to π. So itβs this angle here, marked in orange. We can see that the diagram consists of a triangle, triangle π΅ππ, and then the pentagon π΄π΅πΆπ·πΈ which weβre told is regular. Letβs think about how weβre going to approach this problem.

The angle that weβre looking for, angle π΄π΅π, sits on a straight line with two other angles: angle ππ΅π inside the triangle and angle π΄π΅πΆ inside the pentagon. If we can work out these two other angles, then we can calculate angle π΄π΅π using the fact that angles on a straight line sum to 180 degrees.

Letβs think about the angle in the triangle first of all. Remember, the angle sum in a triangle is always 180 degrees. And as weβve been given the measures of the other two angles, we can calculate the third. So angle ππ΅π is 180 degrees minus 79 degrees minus 64 degrees which is 37 degrees.

Next, letβs think about the angle in the pentagon, angle π΄π΅πΆ. A key fact about polygons is that the sum of their interior angles can be calculated by multiplying 180 by π minus two, where π represents the number of sides in the polygon. Our polygon is a pentagon which has five sides. Therefore, the sum of its interior angles is found by multiplying 180 by three which is 540.

Now this is the sum of all of the interior angles in the pentagon, not the size of each individual angle. The key piece of information given in the question is that π΄π΅πΆπ·πΈ is a regular pentagon. Which means that all of its interior angles are the same size. Therefore, each interior angle can be found by dividing the sum by five. 540 divided by five which is 108 degrees.

So now we know the size of angle π΄π΅πΆ and the size of angle ππ΅π. Remember, these two angles sit on a straight line with angle π΄π΅π, which weβre looking to calculate. So angle π΄π΅π is equal to 180 degrees minus 108 degrees minus 37 degrees. The measure of angle π΄π΅π is 35 degrees.