Question Video: Finding the Measure of an Angle in a Triangle given the Corresponding Angle’s Measure in a Congruent Triangle | Nagwa Question Video: Finding the Measure of an Angle in a Triangle given the Corresponding Angle’s Measure in a Congruent Triangle | Nagwa

# Question Video: Finding the Measure of an Angle in a Triangle given the Corresponding Angleβs Measure in a Congruent Triangle Mathematics • First Year of Preparatory School

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In the following figure, find πβ πππ.

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### Video Transcript

In the following figure, find the measure of angle πππ.

So, letβs have a look at the diagram that weβre given. We could see that there are two lengths, ππ and ππ, which are marked as the same length. We can see that we have two right angles. And we can see that thereβs an angle, πππ, which is marked as 47 degrees. There are two triangles, πππ and πππ. And thereβs a length ππ which is common to both triangles. Letβs see if we can work out if these two triangles are congruent, which means exactly the same shape and the same size.

So, letβs take a look at the two triangles. In both triangle πππ and triangle πππ, there is the length ππ. So, both of these are the same length. They both have an angle of 90 degrees. And in triangle πππ, weβre told that the length ππ is equal to the length of line ππ in triangle πππ. So, it might seem that we could apply the congruency rule, side-angle-side. But in this case, we canβt because the angle isnβt the included angle between the two sides that weβre checking. So, we canβt 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 ππ which is common to both. And the line ππ in triangle πππ is equal to the line ππ in triangle πππ. So, we have a side which is the same length in both triangles. So, weβve shown that our two triangles are congruent by using the hypotenuse-leg congruency rule.

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

And so our final answer is the measure of angle πππ is equal to 43 degrees.

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