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.
