Question

all ......urgent...... plzzxx​

Answer 1

Answer:

qn:1)let angle POR be 5x and angle ROQ be 7x

then5x+7x=180 degree(linear pair)

12x=180

x=180/12

=15 degree

that is,5x=5*15=75 degree

7x = 7*15=105 degree

then,anglePOR=angleSOR=75degree(vertically opposite angle)

also,angleROQ=anglePOS=105degree(vertically opposite angle)

qn:2)let extend rays PQ till T

Now angle TOP +angle POQ =180degrees(linear pair

Adding the equation(1)and(2)

angle TOP +angle POQ+angle TOS +angle SOR+angle QOR=360degrees

since,angle TOP+angle TOS =angle POS

anglePOQ+angleQOR+angleSOR+angle POS=360 degree

Hence,it is proved

qn:3)In TQR

angle TQR=40degree

angle QTR=90degree

Now

x+angle TQR+angleQTR=180degree

x+40degree+90degree=180degree

x+130=180

x=180-130

x=50degree

Now,if we consider,

y is the exterior angle of PSR

y=angleSPR+x(External angle is the sum of 2interior angle)

y=30degree+50degree

y=80degree

Hopes it help for you......