### Video Transcript

Given that π΄π΅πΆπ· is a square and the measure of angle πΈπ·πΆ equals 62 degrees, find the measure of angle π·πΈπ΄.

Letβs start this question by reminding ourselves of some of the properties of a square. We know that a square has four equal length sides and four equal angles that are 90 degrees each. So in our diagram, the square π΄π΅πΆπ· is split into three different triangles. Weβre told that the measure of angle πΈπ·πΆ is 62 degrees. And we need to work out the angle marked pink, that is, the measure of angle π·πΈπ΄. If we look at the triangle π΄π·πΈ, we could, in theory, find our missing angle if we knew the two other angles in this triangle. So letβs have a look and see if we can calculate either of these two angles.

Letβs start by looking at the angle π΄π·πΈ. We can see that itβs part of the larger angle π΄π·πΆ, which is one of the angles on our square. So to find π΄π·πΈ then, we could find our right angle π΄π·πΆ and subtract 62 degrees, which is the angle πΈπ·πΆ. So then we can say that the measure of angle π΄π·πΈ must be 28 degrees. Next, letβs see if we can calculate the measure of angle π·π΄πΈ. We noticed that the line πΆπ΄ is a diagonal of our square. We can recall that the diagonals of a square bisect the angles. The word bisect means to split exactly in two. This means that the 90-degree angles at the vertices of our square will be split into two equal 45-degree angles by the diagonal. This means that the measure of angle π·π΄πΈ must be equal to 45 degrees.

So letβs now return to our triangle π΄π·πΈ and see if we can find the measure of our third missing angle π·πΈπ΄. We can use the fact that the angles in a triangle add up to 180 degrees. So this means that the measure of angle π΄π·πΈ plus the measure of angle π·π΄πΈ plus the measure of angle π·πΈπ΄ must be equal to 180 degrees. We can fill in the angles that we know to give us 28 degrees plus 45 degrees plus the measure of angle π·πΈπ΄ equals 180 degrees. So 73 degrees plus the measure of angle π·πΈπ΄ would be a 180 degrees. So to find the measure of angle π·πΈπ΄, we would subtract 73 from both sides, giving us a 180 degrees minus 73 degrees, giving us 107 degrees. So our final answer for the measure of angle π·πΈπ΄ is 107 degrees.