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Use the figure to determine 𝑚∠𝐷.
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
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.
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