The document Short 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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**Q.1. If P, Q, and R are three collinear points, then name all the line segments determined by them.**

**Ans.**

We can have the following line segments:

**Q.2. In the adjoining figure, identify at least four collinear points.****Ans.** The four collinear points are **A, B, C, and R**.

**Q.3. Find the complement of 36°.**

⇒ Complement of 36°= 90° - 36° = 54°

⇒ Supplement of 105° = 180° - 105° = 75°

**Q.5. Angles ∠ P and 100° form a linear pair. What is the measure of ∠ P?Ans. **∵ The sum of the angles of a linear pair equal to 180°.

∴ ∠ P + 100° = 180° ⇒ ∠ P = 180° - 100 = 80°.

∴ p + 120° = 180° ⇒ p = 180° - 120° = 60°

∴ ∠AOC + ∠COB = 180°

⇒ 63° + x = 180° ⇒ x = 180° - 63° = 117°

**Q.8. In the given figure, AB, CD, and EF are three lines concurrent at O. Find the value of y.Ans. **∵ ∠AOE and ∠BOF and vertically opposite angles.

∴ ∠AOE = ∠BOF = 5y ..... (1)

Now, CD is a straight line,

⇒ ∠COE + ∠EOA + ∠AOD = 180°

⇒ 2y + 5y + 2y = 180° [From (1)]

⇒ 9y = 180°⇒ y = (180°/2)= 20°

Thus, the required value of y is 20°.

**Q.9. In the adjoining figure, AB || CD and PQ is transversal. Find x.****Ans.** ∵ AB || CD and PQ is a transversal.

∴ ∠ BOQ = ∠ CQP [∵ Alternate angles are equal]

⇒ x = 110° [∵ ∠ CQP = 110°]

**Q.10. Find the measure of an angle that is 26° more than its complement.Ans. **Let the measure of the required angle be x.

∴ Measure of the complement of x° = (90° - x)

⇒ x° - (90° - x) = 26°

⇒ x - 90° + x = 26°

⇒ 2x = 26° + 90° = 116°

⇒ x = (116°/2) = 58°

Thus, the required measure = 58°.

**Q.11. Find the measure of an angle if four times its complement is 10° less than twice its complement.**

∴ Its complement = (90° - x) and Its supplement = (180° - x)

According to the condition:

4(Complement of x) = 2(Supplement of x) - 10

⇒ 4(90° - x) = 2(180° - x) - 10°

⇒ 360° - 4x = 360° - 2x - 10°

⇒ 4x - 2x = 360° - 360° + 10°

⇒ 2x = 10° ⇒ x = (10°/2)= 5°

Thus, the measure of the required angle is 5°.

**Q.12. Two supplementary angles are in the ratio 3:2. Find the angles.**

∵ They are supplementary angles.

∴ 3x + 2x = 180°

⇒ 5x = 180° ⇒ x = (180°/5) = 36°

∴ 3x = 3 x 36° = 108° and 2x = 2 x 36° = 72°

Thus, the required angles are 108° and 72°.

**Q.13. In the adjoining figure, AOB is a straight line.**

**Ans.** ∵ AOB is a straight line.

∴ ∠ AOC + ∠ BOC = 180°

⇒ (3x + 10°) + (2x - 30°) = 180° [Linear pair]

⇒ 3x + 2x + 10° - 30° = 180°

⇒ 5x - 20° = 180°

⇒ 5x = 180° + 20° = 200° ⇒ x = (200°/5) = 40°

Thus, the required value of x is 40°.

**Q.14. In the adjoining figure, find ∠ AOC and ∠ BOD.Ans. **∵ AOB is a straight line.

∴ ∠AOC + ∠COD + ∠DOB =180°

⇒ x + 70° + (2x - 25°) = 180°

⇒ x + 2x = 180° + 25° - 70°

⇒ 3x = 205° - 70° = 135° ⇒ x = (135°/3) = 45°

∴ ∠ AOC = 45°

⇒ ∠ BOD = 2x - 25° = 2 (45°) - 25° = 90° - 25° = 65°

**Q.15. In the adjoining figure, AB || CD. Find the value of x.****Ans.** Let us draw EF || AB and passing through point O.

∴ EF || CD and CO is a transversal.

⇒ ∠ 1 = 25° [Alternate angles]

Similarly, ∠ 2 = 35°

Adding, ∠ 1 + ∠ 2 = 25° + 35° ⇒ x = 60°

Thus, the required value of x is 60°.

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