Question

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Answer 1

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Answer 2

Ans 1 :- POY = 90°

POX + POY = 180° ( If a ray stand on line then the sum of two adjacent angle so formed is 180° )

POX + 90° = 180°
POX = 180° - 90
=. 90°

We are given that ZX a : b = 2 : 3
then a = 90° x 2/5
= 36°
b = 90° x 3/5
= 54°

Now angle = XON = MOY
( vertically opposite angle MOY = MOP + POY )
= MOD + POY
= a + 90°
= 36° + 90°
= 126 °
Therefore c = 126°


Ans 2 :- Given :- PQR = PRQ

To prove = PQS = PRT

Proof :-
PQR = PRQ = x ( Let this be x ) ( i )
Now , PQS + PQR = 180°
and PRT + PRQ = 180°

PQS + PQR = PRT + PRQ ( :- each 180° )
PQS + x = PRT + x
so , PQS = PRT .

Ans 3 :- Since sum of all t angle round a point is equal to 360° . Therefore ,

x + y + z + w = 360°

( x + y ) + ( z + w ) = 360°

( x + y ) + ( x + y ) = 360°

2( x + y ) = 360°

x + y = 180 °

AOB is a straight line .


Ans 4 :- Given :- PQ , a line . OR , a ray

To Prove :- ROS = 1/2 ( QOS - PQS )

Proof :-

In the fig , we have
QOS = ROS + QOR ( i )
POS = POR - ROS ( ii )

By the subtracting equation ( ii ) from ( i )
QOS - POS = ( ROS + QOR ) - ( POR - ROS )
= ROS + QOR - POR + ROS
QOS - POS = 2 ROS
1/2 ( QOS - POS ) = ROS .

Ans 4 :-