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

Bethani Gasparine

Use the figure to determine 𝑚∠𝐷.


Video Transcript

Use the figure to determine the measure of angle 𝐷.

In our figure, we can see that two of the sides are congruent: 𝐴𝐹 is congruent to 𝐵𝐹 and 𝐷𝐹 is congruent to C𝐹. Angle 𝐴𝐹𝐷 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 𝐵 will be equal to angle 𝐴. The reason why is because angle 𝐵 is between the two sides, where there is a two marking and the side that has no marking, and angle 𝐴 is between the two marking and no marking. Therefore, these two angles are corresponding, meaning they’re in the same spots. So angle 𝐴 is 55 degrees.

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

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