The document Very Short Answer Type Questions- Lines and Angles Class 9 Notes | EduRev is a part of the Class 9 Course Class 9 Mathematics by VP Classes.

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**Q.1. What is the measure of an angle whose measure is 32° less than its supplement?Sol. **Let the required angle be x

∴ x = (180°- x) - 32°

⇒ x = 74°

Sol.

∴ (180°- x) = 4 (90° - x)

⇒ x = 60°

Sol.

∴ x + x = 110°

⇒ x = 55°

Sol.

⇒ ∠B = ∠C

Also, ∠A = 90°

⇒ ∠B + ∠C = 90°

⇒ ∠B = ∠C = (90

Sol.

∴ ∠1 + 70° = 180° [co-interior angles]

⇒ ∠1 = 180° - 70° = 110°

Now, 2x = 110° [vertically opposite angles]

⇒ x =(110°/2) = 55°**Q.6. If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2 : 3 then, what is the smaller angle?Sol. **ℓ || m and p is the transversal

∴ ‘a’ and ‘b’ are interior angles on the same side of the transversal p.

Let a = 2x and b = 3x

∴ a + b = 180°

⇒ 2x + 3x = 180°

⇒ 5x = 180°

⇒ x = (180/5)= 36°

∴ smaller angle = 2x = 2 x 36 = 72°**Q.7. In the figure, what is the measure of ∠ ABC?Sol. **

Now, ext. ∠ACR= ∠ABC + ∠BAC = 105°

⇒ ∠ABC = 105° - 45° = 60°**Q.8. In the following figure AB || CD. Find the measure of ∠BOC.**

**Sol. **Extending AB to intersect OC, we get the following figure.

ABF is a straight line

∴ ∠OBF = 180° - 165° = 15°

AB || CD ⇒ EF || CD

∴ ∠1 + 75° = 180°

⇒ ∠1 = 180° - 75° = 105°

⇒ ∠2 = 105°

Now, in **Δ**, ∠2 + 15° + ∠BOC = 180°

⇒ 105° + 15° + ∠BOC = 180°

⇒ ∠BOC = 180° - 105° - 15°

= 60°

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