### Video Transcript

In the following figure, find the measure of angle πππ.

So, letβs have a look at the diagram that weβre given. We could see that there are two lengths, ππ and ππ
, which are marked as the same length. We can see that we have two right angles. And we can see that thereβs an angle, πππ
, which is marked as 47 degrees. There are two triangles, πππ and πππ
. And thereβs a length ππ which is common to both triangles. Letβs see if we can work out if these two triangles are congruent, which means exactly the same shape and the same size.

So, letβs take a look at the two triangles. In both triangle πππ and triangle πππ
, there is the length ππ. So, both of these are the same length. They both have an angle of 90 degrees. And in triangle πππ, weβre told that the length ππ is equal to the length of line ππ
in triangle πππ
. So, it might seem that we could apply the congruency rule, side-angle-side. But in this case, we canβt because the angle isnβt the included angle between the two sides that weβre checking. So, we canβt use the side-angle-side rule.

However, since both triangles have a 90-degree angle, this means that they are right triangles. So, we can check if we could apply the congruency rule, HL, for hypotenuse and leg. In this case, the longest side, the hypotenuse of both triangles, is the line ππ which is common to both. And the line ππ in triangle πππ is equal to the line ππ
in triangle πππ
. So, we have a side which is the same length in both triangles. So, weβve shown that our two triangles are congruent by using the hypotenuse-leg congruency rule.

So now, letβs look at putting some of the information into our diagram. Since the triangles are congruent, we know that triangle πππ must also have a 47-degree angle. But which one of them is equal to 47? In triangle πππ
, our 47-degree angle sits between the hypotenuse and the line ππ
. Therefore, in triangle πππ, the 47-degree angle must also be between the hypotenuse and the congruent side ππ. In the question, weβre asked to calculate the measure of angle πππ. And we could do this by remembering that the angles in a triangle add up to 180 degrees. This means that the angle πππ is equal to 180 take away the sum of 90 and 47.

And so our final answer is the measure of angle πππ is equal to 43 degrees.