Very Short Answer Type Questions: Lines & Angles

# Class 9 Maths Chapter 6 Question Answers - Lines and Angles

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°

Q.2. If the supplement of an angle is 4 times its complement, find the angle.
Sol.
Let the required angle be x
∴  (180°- x) = 4 (90° - x)
⇒ x = 60°

Q.3. An exterior angle of a Δ is 110° and its two opposite interior angles are equal. What is the measure of each angle?
Sol.
Let each of the interior opposite angle be x
∴ x + x  = 110°
⇒ x = 55°

Q.4. In a rt. ΔABC, ∠A = 90° and AB = AC. What are the values of ∠B and ∠C?
Sol.
∵ AB = AC
⇒ ∠B = ∠C
Also, ∠A = 90°
⇒ ∠B + ∠C = 90°
⇒ ∠B = ∠C = (90o/2) = 45°

Q.5. In the figure, what is the value of x?
Sol.
∵ ℓ || m and p is a transversal

∴ ∠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.
PAQ = ∠BAC     [vertically opp. angles]

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°

The document Class 9 Maths Chapter 6 Question Answers - Lines and Angles is a part of the Class 9 Course Mathematics (Maths) Class 9.
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## Mathematics (Maths) Class 9

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## FAQs on Class 9 Maths Chapter 6 Question Answers - Lines and Angles

 1. What are lines and angles?
Ans. Lines and angles are basic geometrical concepts. A line is a straight path that extends infinitely in both directions. An angle is formed when two lines or line segments meet at a common point.
 2. What is the difference between a line and a line segment?
Ans. A line extends infinitely in both directions, whereas a line segment is a finite portion of a line with two distinct endpoints.
 3. How do you classify angles based on their measurements?
Ans. Angles can be classified as acute angles (less than 90 degrees), right angles (exactly 90 degrees), obtuse angles (between 90 and 180 degrees), or straight angles (exactly 180 degrees).
 4. What are complementary angles?
Ans. Complementary angles are two angles that add up to 90 degrees. In other words, when the measures of two angles sum up to 90 degrees, they are called complementary angles.
 5. How do you identify parallel lines?
Ans. Parallel lines are lines that never intersect or cross each other. They have the same slope and can be identified by their arrows or by using a transversal line to form congruent corresponding angles.

## Mathematics (Maths) Class 9

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