tarek99 wrote:

In the figure shown, the measure of angle PRS is how many degrees greater than the measure of angle PQR?

(1) The measure of angle QPR is 30 degrees

(2) The sume of the measures of angles PQR and PRQ is 150 degrees

Can someone show me how to solve this problem? the OA is D, but how? I chose E.

thanks

<S is 90 degree, hope this is correct

PQR + QPS = 90 ---(1)

RPS + PRS = 90 ---(2)

both are because of internal angles of triangle = 180, and S is 90

What we want to find is PRS - PQR

we equate (1) and (2)

PQR + QPS = RPS + PRS

Thus PRS - PQR = QPS - RPS

so if we know difference between QPS and RPS, then we know the answer

1) QPR = 30

QPR = QPS - RPS = 30 - sufficient

2) tells that QPR = 30 from internal angles of triangle, thus sufficient

answer D