# PQRS is a parallelogram whose diagonals intersect at M.

If ∠PMS=54°, ∠QSR=25°, ∠SQR=30°, FIND: i)∠RPS (ii) ∠PRS (iii) ∠PSR

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If ∠PMS=54°, ∠QSR=25°, ∠SQR=30°, FIND: i)∠RPS (ii) ∠PRS (iii) ∠PSR

plz fast

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∠rps=180-∠pms-∠qsp

=180-54-30=97

∠PRS=180-97-55=28

∠PSR=30+25

=180-54-30=97

∠PRS=180-97-55=28

∠PSR=30+25

The Brainliest Answer!

<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