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In parallelogram PQRS, the measure of angle P is five times the measure of angle Q. What is the measure of angle R, in degrees?

 May 29, 2020
 #1
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The consecutive angles of a parallelogram are supplementary   --->         angle(P) + angle(Q)  =  180o

           angle(P)  =  5 · angle(Q)                                                    --->   5 · angle(Q) + angle(Q)  =  180o

                                                                                                                                 6 · angle(Q)  =  180o

                                                                                                                                      angle(Q)  =  30o

 

--->   angle(P)  =  150o 

 

Since the opposite angles of a parallelogram are congruent   --->   angle(R)  =  angle(P)  =  150o

 May 29, 2020
 #2
avatar+9682 
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In parallelogram PQRS, the measure of angle P is five times the measure of angle Q. What is the measure of angle R, in degrees?

 

Hello Guest!

 

\(180\ degrees-5Q=Q\\ 6Q=180\ degrees\\ Q=30\ degrees\)

\(R=5Q\\ R=5\cdot 30^0\)

\(R=150\ degrees\)

laugh  !

 May 29, 2020

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