For the figure, as marked, what is m∠R? Show your solution.

Question

Answer 1

Hi Beaux S

First, the angle measures are difficult to see in your figure, I tried printing your figure but the numbers were still hard to see but and please correct me if I am wrong.

P = 60°

T = 70°

Q looks like it be could 30 or 50°

S = 30°

Since the first two angle measures inside triangle PTQ along line PQR are given, to solve the problem you want to find the measure of the missing angle in triangle PTQ and proceed from there by making sure all the angles adjacent to angle Q along line PQR sum to 180 and that triangle QSR sums to 180. Please see below;

The measure of angle P along line PQR inside triangle PTQ looks like 60 degrees, if that is correct then for your larger triangle, PTQ the measure of the second angle along line PQR inside triangle PTQ

180 -(60 + 70)= 180 -130 = 50°

50 + Q = 50 + 30 = 80°

The angle inside your next triangle QSR along line PQR is supplemental to 80 so,

180 - 80 = 100°

Finally, since triangle QSR must sum to 180 then measure of R the last angle along line PQR inside triangle QSR is

180 -(100 + S) = 180-(100 + 30) = 180-130 = 50

R = 50°

I hope this helps and please let me know if I interpreted the numbers in your figure correctly.