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Geometry - Solved Examples
Answer - D
Explanation
A line has no points.
Q 2 - A line segment has
Answer - B
Explanation
A line segment has two end points.
Answer - A
Explanation
A ray has one end point.
Q 4 - An angle which is greater then 180° but less than 360° is called
Answer - B
Explanation
An angle which is greater than 180° but less than 360° is called a reflex angle.
Answer - B
Explanation
Complement of 62°= (90° – 62°) = 28°.
Answer - B
Explanation
Supplement of 60° = (180°-60°) =120°.
Answer - C
Explanation
Complement of 72° 40' = (90°-72° 40') =17° 20'.
Q 8 - An angle is one fifth of its supplement. The measure of the angle is
Answer - B
Explanation
x = 1/5 (180 – x )⇒ 5x = 180 – x ⇒ 6x = 180 ⇒ x = 30°.
Q 9 - If an angle is its own complementary angle, then its measure is
Answer - B
Explanation
x=(90-x) ⇒ 2x = 90 ⇒ x = 45° .
Answer - D
Explanation
The angle are ∠AOB , ∠BOC,∠COD,∠DOE,∠AOC,∠AOD, ∠AOE,∠BOD,∠BOD,∠COE. Thus , 10 angle are formed.
Q 11 - An angle is 24° more than its complement.The measure of the angle is
Answer - A
Explanation
x – (90-x ) = 24 ⇒ 2x = 114 ⇒ x = 57 ∴ Required angle is 57°.
Q 12 -An angle is 32° less than its supplement. The measure of the angle is
Answer - A
Explanation
(180 –X) – X = 32 ⇒ 2x = 180 – 32 = 148 ⇒ x = 74. Required angle is 74°.
Q 13 - Two Supplementary angles are in th ratio 3:2. The smaller angle measures
Answer - C
Explanation
Let the measures of the angle be (3x)° and (2x)°. Then, 3x+2x=180 ⇒ 5x = 180 ⇒ x = 36. Smaller angle = (2x)° = (2*36)° = 72°.
Q 14 - In the given figure, AOB is a straight line, ∠AOC = 68° and ∠BOC = x°. The value of the x is
Answer - A
Explanation
Since ∠AOB is a straight angle , we have X+ 68 = 180 ⇒ x= (180-68)° = 120°
Q 15 - In the given figure , AOB is a straight line, ∠AOC = (3x+20)° and ∠ BOC =(4 x-36)°. The value of the x is
Answer - B
Explanation
Since ∠AOB is a straight angle , we have ∠AOC + ∠ BOC =180° ⇒ 3x + 20 +4x – 36 = 180 ⇒ 7x = 164 ⇒ x = 22.
Q 16 - In the given figure , AOB is a straight line, ∠ AOC = (3x-8)° and ∠COD =50 and ∠BOD° =(x+10)°. The value of the x is
Answer - A
Explanation
Since ∠AOB is a straight angle , we have ∠AOC + ∠ COB + ∠ BOD = 180° ⇒ (3X – 8)° + 50° + (X+ 10)° = 180° ⇒ 4X = 128 ⇒ X = 32.