Jharkhand Board JAC Class 9 Maths Important Questions Chapter 6 Lines and Angles Important Questions and Answers.

## JAC Board Class 9th Maths Important Questions Chapter 6 Lines and Angles

Question 1.

Two supplementary angles are in the ratio 4 : 5, find the angles.

Solution :

Let angles be 4x and 5x.

∵ Angles are supplementary

∴ 4x + 5x = 180°

⇒ 9x = 180°

⇒ x = \(\frac {180°}{2}\) = 20°

∴ Angles are 4 × 20° and 5 × 20° i.e., 80° and 100°

Question 2.

If an angle differs from its complement by 10°, find the angle.

Solution :

Let angle be x° then its complement is 90° – x°.

Now given, x° – (90° – x°) = 10°

⇒ x° – 90° + x° = 10°

⇒ 2x° = 10° + 90° = 100°

⇒ x° = \(\frac {100°}{2}\) = 50°

∴ Required angle is 50°.

Question 3.

In figure, OP and OQ bisects ∠BOC and ∠AOC respectively. Prove that ∠POQ = 90°.

Solution :

∵ OP bisects ∠BOC

∴ ∠POC = \(\frac {1}{2}\)∠BOC ………(i)

Also OQ bisects ∠AOC

∠COQ = \(\frac {1}{2}\)∠AOC ………(ii)

∵ OC stands on AB

∴ ∠AOC + ∠BOC = 180°[Linear pair]

⇒ \(\frac {1}{2}\)∠AOC + \(\frac {1}{2}\)∠BOC = \(\frac {1}{2}\) × 180°

⇒ ∠COQ + ∠POC = 90° [Using (i) and (ii)]

⇒ ∠POQ = 90°

Question 4.

In figure, lines AB, CD and EF intersect at O. Find the measures of ∠AOC, ∠DOE and ∠BOF.

Solution :

Given, ∠AOE = 40° and ∠BOD = 35°

Clearly, ∠AOC = ∠BOD

(Vertically opposite angles)

⇒ ∠AOC = 35°

⇒ ∠BOF = ∠AOE

[Vertically opposite angles]

⇒ ∠BOF = 40°

Now, ∠AOB = 180° [Straight angle]

⇒ ∠AOC + ∠COF + ∠BOF = 180°

[Angles sum property]

⇒ 35° + ∠COF + 40° = 180°

⇒ ∠COF = 180° – 75° = 105°

Now, ∠DOE = ∠COF

[Vertically opposite angles]

∴ ∠DOE = 105°

Question 5.

In figure if l || m, n || p and ∠1 = 85° find ∠2.

Solution :

∵ n || p and m is transversal

∴ ∠1 = ∠3 = 85° [Corresponding angles]

Also, m || l and p is transversal

∴ ∠2 + ∠3 = 180°

[Consecutive interior angles]

⇒ ∠2 + 85° = 180°

⇒ ∠2 = 180° – 85°

⇒ ∠2 = 95°

Multiple Choice Questions

Question 1.

If two lines are intersected by a transversal, then each pair of corresponding angles so formed is

(a) Equal

(b) Complementary

(c) Supplementary

(d) None of these

Solution :

(a) Equal

Question 2.

Two parallel lines have:

(a) a common point

(b) two common points

(c) no common point

(d) infinite common points

Solution :

(c) no common point

Question 3.

An angle is 14° more than its complement then angle is:

(a) 38°

(b) 52°

(c) 50°

(d) none of these

Solution :

(a) 38°

Question 4.

The angle between the bisectors of two adjacent supplementary angles is:

(a) acute angle

(b) right angle

(c) obtuse angle

(d) none of these

Solution :

(c) obtuse angle

Question 5.

If one angle of triangle is equal to the sum of the other two then triangle is:

(a) acute triangle

(b) obtuse triangle

(c) right triangle

(d) none of these

Solution :

(c) right triangle

Question 6.

Point x is in the interior of ∠BAC. If ∠BAC = 70° and ∠BAX = 42° then ∠XAC =

(a) 28°

(b) 29°

(c) 27°

(d) 30°

Solution :

(a) 28°

Question 7.

If the supplement of an angle is three times its complement, then angle is:

(a) 40°

(b) 35°

(c) 50°

(d) 45°

Solution :

(d) 45°

Question 8.

Two angles whose measures are a and b are such that 2a – 3b = 60° then \(\frac {4a}{5b}\) = _______, if they form a linear pair :

(a) 0

(b) 8/5

(c) \(\frac {12}{5}\)

(d) \(\frac {2}{3}\)

Solution :

(c) \(\frac {12}{5}\)

Question 9.

Which one of the following statements is not false?

(a) If two angles are forming a linear pair, then each of these angles is of measure 90°

(b) Angles forming a linear pair can both be acute angles.

(c) One of the angles forming a linear pair can be obtuse angle.

(d) Bisectors of the adjacent angles form a right angle.

Solution :

(c) One of the angles forming a linear pair can be obtuse angle.

Question 10.

Which one of the following is correct?

(a) If two parallel lines are intersected by a transversal, then alternate interior angles are equal

(b) If two parallel lines are intersected by a transversal then sum of the interior angles on the same side of transversal is 180°

(c) If two parallel lines are intersected by a transversal then corresponding angles are equal.

(d) All of these

Solution :

(d) All of these