Find the measure of the indicated angle to the nearest degree
1 answer:
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Answer:
C, 20 units
Step-by-step explanation:
We see that both angles QRS and QTR are 90 degrees. In addition, angles SQR and RQT are equivalent (because they're both angle Q).
By AA Similarity, we know that triangle QTR is similar to triangle QRS.
With this similarity in mind, we can look at the ratios of corresponding lengths to set up a proportion. QR from triangle QTR is the hypotenuse, and it corresponds to hypotenuse QS from triangle QRS. So, we can write the ratio x/(9 + 16) = x/25.
Now, we see that long leg QT of triangle QTR corresponds to long leg QR of triangle QRS. So, another ratio we can write is: 16/x.
Finally, we set these two ratios equal to each other:
Cross-multiplying, we get: .
Thus, x = . The answer is C, 20 units.
Hope this helps!