Question

Given DEFGH ≅ QRSTU .



What is the measure of ∠R ?



Enter your answer in the box.


m∠R =
°

Answer 1

Using our congruency statement DEFGH ≅ QRSTU, we can see which angles map onto each other. 

D ≅ Q
E ≅ R
F ≅ S
G ≅ T
H ≅ U

We see that E ≅ R, and since E is 143 degrees, R = 143 degrees.

Why is this true, you may ask? When dealing with congruency, the given points/letters (they are really both) are congruent to the corresponding shapes letter/point. For example, if triangle ABC ≅ DEF, A would correspond to D, B would correspond to E, etc. When you see these types of problems, congruency will be applied to angles (it could apply to lines in other cases).

If you have any questions, feel free to ask!

:)

Answer 2

Confirmation.The correct answer is <R = 143.

If you look at both the shapes, they have equal sides and are congruent. The only thing confusing about it is the rotation and transformation, so all you have to do is draw it as the original image and you will recognize that the shapes are congruent .

Now that you know the shapes are congruent, you look at the angles.Sense the chape is congruent, that means all the angles from that shape are the same angles for the other so therefore:

<Q = 60 degrees

<T = 102 degrees

<S = 90 degrees

<U = 145 degrees

<R = 143 degrees is the correct answer.

Hope it helps and have a nice day/night!