The document Long Answer Type Questions- Lines and Angles Class 9 Notes | EduRev is a part of the Class 9 Course Mathematics (Maths) Class 9.

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**Question 1. In the adjoining figure, AB || CD. If ∠ APQ = 54° and ∠ PRD = 126°, then find x and y. Solution: **∵ AB || CD and PQ is a transversal, then interior alternate angles are equal.

⇒ ∠ APQ = ∠ PQR

⇒ 54° = x [∵ ∠ APQ = 54° (Given)]

Again, AB || CD and PR is a transversal, then ∠ APR = ∠ PRD [Interior alternate angles]

But ∠ PRD = 126° [Given]

∴ ∠ APR = 126°

Now, exterior∠ PRD = x + y

⇒ 126° = 54° + y

⇒ y = 126° - 54° = 72°

Thus, x = 54° and y = 72°.

**Question 2. In the adjoining figure AB || CD || EG, find the value of x. Solution:** Through E, let us draw FEG || AB || CD.

Now, since FE || AB and BE is a transversal.

∴ ∠ ABE + ∠ BEF = 180°

[Interior opposite angles]

⇒ 127° + ∠ BEF = 180°

⇒ ∠ BEF = 180° ∠ 127° = 53°

Again, EG || CD and CE is a transversal.

∴ ∠ DCE + ∠ CEG = 180° [Interior opposite angles]

⇒ 108° + ∠ CEG = 180° ⇒ ∠ CEG = 180° - 108° = 72°

Since FEG is a straight line, then

⇒ ∠BEF + ∠BEC + ∠CEG = 180° [Sum of angles at a point on the same side of a line = 180°]

⇒ 53° + x + 72°

= 180°

⇒ x = 180° - 53° - 72°

= 55°

Thus, the required measure of x = 55°.

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