Ex 6.2 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev

Mathematics (Maths) Class 9

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Class 9 : Ex 6.2 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev

The document Ex 6.2 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev is a part of the Class 9 Course Mathematics (Maths) Class 9.
All you need of Class 9 at this link: Class 9

Question 1. In the following figure, find the values of x and y and then show that AB || CD.

Ex 6.2 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev

Solution: In the figure, we have CD and PQ intersect at Y.

Ex 6.2 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev

∴ y = 130º                       [Vertically opposite angles]
Again, PQ is a straight line and EA stands on it.
∴ ∠ AEP + ∠ AEQ = 180º            [Linear pair]
or 50º + x = 180º
⇒ x = 180º -  50º = 130º                   …(2)
From (1) and (2), x = y
But they are the angles of a pair of interior alternate angles.
∴ AB || CD.


Question 2. In the following Figure, if AB || CD, CD ||EF and y : z = 3 : 7, find x.

Ex 6.2 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev

Solution:              Ex 6.2 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev

Ex 6.2 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev

∴ AB || EF and PQ is a transversal.
∴ Interior alternate angles are equal.
∴ ∠ x= ∠ z                           …(1)
Again, AB || CD,
∴ Interior opposite angles are supplementary,
⇒ y + z = 180º
But y : z = 3 : 7

Ex 6.2 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev

From (1) and (2), we have x = 126º


Question 3. In the following figure, if AB || CD, EF ⊥ CD and ∠ GED = 126º, find ∠ AGE, ∠ GEF and ∠ FGE.
 Solution:
AB || CD and GE is a transversal.

Ex 6.2 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev

∴ Interior alternate angles are equal.
∴ ∠ AGE = ∠ GED
But ∠ GED = 126º                [Given]
∴ ∠ AGE = 126º
Since ∠ GED = 126º
∴ ∠ GEF + ∠ FED = ∠ GED
or ∠ GEF + 90º = 126º
or ∠ GEF = 126 ∠ 90° = 36º
Next, AB || CD and GE is a transversal.
∴ ∠ FGE + ∠ GED = 180º
or ∠ FGE + 126º = 180º
or ∠ FGE = 180º - 126º = 54º
Thus, ∠ AGE = 126º, ∠ GEF = 36º and ∠ FGE = 54º


Question 4. In the following figure, if PQ || ST, ∠ PQR = 110º and ∠ RST = 130º, find ∠ QRS.
 Hint: Draw a line parallel to ST through point R.

Ex 6.2 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev

Solution: ∵ PQ || ST [Given] and EF || ST [Construction] ∴ PQ || EF
and QR is a transversal,

Ex 6.2 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev

∴ Interior alternate angles are equal i.e ∠ PQR = ∠ QRF
But ∠ PQR = 110º                    [Given]
∴ ∠ QRF = ∠ QRS + ∠ SRF = 110º              …(1)
Again ST || EF [Construction] and RS is a transversal.
∴ ∠ RST + ∠ SRF = 180º
or 130º + ∠ SRF = 180º
⇒ ∠ SRF = 180º - 130º = 50º
Now, from (1), we have
∠ QRS + 50º = 110º
⇒ ∠ QRS = 110º - 50º = 60º
Thus, ∠ QRS = 60º.


Question 5. In the following figure, if AB || CD, ∠ APQ = 50º and ∠ PRD = 127º, find x and y.            
 Solution: 
We have AB || CD [Given] and PQ is a transversal.

Ex 6.2 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev

∴ Interior alternate angles are equal.
∴ ∠ APQ = ∠ PQR
or 50º = x [∵ APQ = 50º                    (Given)] ….(1)
Again, AB || CD and PR is a transversal.
∴ ∠ APR = ∠ PRD                       [Interior alternate angles]
⇒ ∠ APR = 127º                         [∵ It is given that ∠ PRD = 127º]
But ∠ APR = ∠ APQ + ∠ QPR
∴ ∠ APQ + ∠ QPR = 127º
⇒ 50º + y = 127º                       [∵ It is given that ∠ APQ = 50º]
⇒ y = 127º - 50º = 77º
Thus, x = 50º and y = 77º


Question 6. In the following figure, PQ and RS are two mirrors placed parallel to each other. An incident ray AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes the mirror RS at C and again reflects back along CD. Prove that AB || CD.

Ex 6.2 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev

Solution:
 REMEMBER

(i) Perpendiculars to the parallel lines are parallel.
(ii) According to the laws of reflection, angle of incidence = angle of reflection
Ex 6.2 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev

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