Question

PQRS is a parallelogram whose diagonals intersect at M.
If ∠PMS=54°, ∠QSR=25°, ∠SQR=30°, FIND: i)∠RPS (ii) ∠PRS (iii) ∠PSR
plz fast

Answer 1

∠rps=180-∠pms-∠qsp
=180-54-30=97
∠PRS=180-97-55=28

∠PSR=30+25

Answer 2

<SQR=<QSP=30

A/C TO ANGLE SUM PROPERTY

<PMS+<QSP+<RPS=180

54+30+<RPS=180

<RPS=180-84=96     ----------(i)

<QSRR+<QSP=<PSR=25+30=55  -----------(iii)

<SMR+<PMS=180     (LINEAR PAIR)

54+<SMR=180

<SMR=180-54=126

<SMR+<QSR+<PRS=180     (ANGLE SUM PROPERTY)

126+25+<PRS=180

<PRS=180-151=29   ---------------(ii)

ANSWER

(i)<RPS=96
(ii)<PRS=29
(iii)<PSR=55