**Q.1Â Â Â In figure , lines AB and CD intersect at O. If and , find and reflex .**

Since OA and OB are opposite rays. Therefore AB is a line.

Since ray OC stands on AB. Therefore,

[Linear Pairs]

[Since ]

[Since (Given)]

Therefore Reflex

Since OC and OD are opposite rays. Therefore CD is a line.

Since ray OE stands on CD. Therefore -

[Linear Pairs]

[Since ]

[Since (Given)]

Hence,

and

**Q.2Â Â Â Â Â Â In figure , lines XY and MN intersect at O. If and a : b = 2 : 3, find c.**

Since a : b = 2 : 3 and a + b = = 90Âº and sum of ratios = 2 + 3 = 5

Therefore

and

Since OM and ON are opposite rays. Therefore MN is a line.

Since ray OX stands on MN. Therefore,

[Linear Pairs]

Hence ,

**Q.3Â Â Â Â Â Â In figure , then prove that .**

Since QS and QR are opposite rays. Therefore, SR is a line.

Since QP stands on the line SR.

Therefore [Linear Pair] ...(1)

Again RQ and RT are opposite rays. Therefore, QT is a line.

Since PR stands on the line QT.

Therefore [Linear Pair] ... (2)

From (1) and (2), we have

[Since Each side = 180Âº] ... (3)

Also Â Â Â Â Â Â (given)Â Â Â Â Â ................(4)

Subtracting (4) from (3), we have

**Q.4Â Â Â Â Â Â In figure, if x + y = w + z, then prove that AOB is a line.**

We know that the sum of all angles around a point is equal to Â 360Âº

Therefore

But [Given]

ThereforeÂ

Thus , form linear pairs. Consequently OA and OB are two opposite rays.

Therefore AOB is a straight line.

**Q.5Â Â Â Â Â Â In figure POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that **

Since OR is perpendicular to the line PQ.

Therefore [Since Each = 90Âº]

**Q.6Â Â Â Â Â It is given that and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects and reflex .
**

Since XY is produced to point P. Therefore XP is a straight line.

Since YZ stands on XP.

Therefore [Linear Pair]

[Since ]

Since ray YQ bisects

Contact Us

Lots of Thanks [LOT]

Very helpfull

good for you very strong formulas

It's very nice and helpful...

Very nice app for students

It's very helpful to study at last time with short notes which are available here... Thanks

It's very helpful

Reallyy helped thank u so much

Zabardast

good solution for questions. nice one..

Really it was very helpfull

It was very nice i love it

it is vvvvvvvvgood it is helpful in exam time

its really great sites for learning and good notes

USEFUL AND HELPFUL

Its very nice and helpful....:-P

It's very nice and useful:-P

It is very nice and helpful:-P

Its very nice and useful for students