Question

In the given figure lines PQ and RS intersect each other at point O. if LPOR:LROQ= 5:7,find all the angles

Answer 1

POR and ROQ are on the straight line they are linear pair.


5x+7x =180

12x=180

X=180/12

X=15

5x=5(15)=75

7x =7(15)=105

ANGLE POR=75°

ANGLE ROQ=105°

ANGLE SOQ=75°(VERTICALLY OPPOSITE ANGLES)

ANGLE POS=105°(V.O.A.)

Answer 2

here two line segment are intersect each other ,PQ and RS.
therefore ➢
angle POR = angle SOQ (vertically opposite angle )
angle on line segment pQ is linear angle
therefore ➢
anglePOR+angleROQ=180° ........eq(1)

angle POR:angleROQ=5:7 (given)
so let
angle POR= 5x
angleQOR=7x
now put these value in equation eq ...1
we get
5x+7x= 180°
12x=180
x=180/12
x= 15°

so the angle POR = 5x= 5×15°=75°
angle QOR=7x=7×15°=105°