# Question Video: Finding the Measure of an Angle in a Triangle given the Corresponding Angleโs Measure in a Congruent Triangle Mathematics • 8th Grade

Use the figure to determine ๐โ ๐ท.

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### Video Transcript

Use the figure to determine the measure of angle ๐ท.

In our figure, we can see that two of the sides are congruent: ๐ด๐น is congruent to ๐ต๐น and ๐ท๐น is congruent to C๐น. Angle ๐ด๐น๐ท is going to be 63 degrees because these two angles are vertical, and vertical angles are congruent.

So since we have two sides that are congruent and an included angle, meaning there between the two sides are congruent, these two triangles are congruent. So that means their corresponding parts are congruent. So angle ๐ต will be equal to angle ๐ด. The reason why is because angle ๐ต is between the two sides, where there is a two marking and the side that has no marking, and angle ๐ด is between the two marking and no marking. Therefore, these two angles are corresponding, meaning theyโre in the same spots. So angle ๐ด is 55 degrees.

Now, our last step is to find the measure of angle ๐ท. And we can do that because in any triangle all three angles will add up to 180 degrees. So the measure of angle ๐ด plus the measure of angle ๐น plus the measure of angle ๐ท will equal 180 degrees.

We can replace the measure of angle ๐ด with 55 degrees and the measure of angle ๐น with 63 degrees. Now we need to add those numbers. 55 plus 63 is 118. Now to solve for the measure of angle ๐ท, we need to subtract 118 from both sides of the equation. And 180 minus 118 is 62; therefore, the measure of angle ๐ท is equal to 62 degrees.
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