Geometry - Online Quiz



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Following quiz provides Multiple Choice Questions (MCQs) related to Geometry. You will have to read all the given answers and click over the correct answer. If you are not sure about the answer then you can check the answer using Show Answer button. You can use Next Quiz button to check new set of questions in the quiz.

Questions and Answers

Q 1 - Two Lines AB and CD intersect at O. If ∠AOC =50⁰,Then ∠ BOD and ∠AOD are respectively

q 17

A - 130⁰ ,50⁰

B - 50⁰, 130⁰

C - 60⁰, 120⁰

D - 40⁰, 140⁰

Answer : B

Explanation

∠ BOD=∠ AOC (vert . opp.  ∠s) =50⁰
∠AOC +∠AOD = 180⁰ ⇒ 50⁰ +∠AOD= 180⁰ ⇒∠AOD=130⁰
∴ ∠ BOD= 50⁰ and ∠AOD = 130⁰.

Q 2 - Two angles are complementary, if the sum of their measures is

A - 90⁰

B - 100⁰

C - 180⁰

D - 360⁰

Answer : A

Explanation

Two angle are complementary, if the sum of their measures is 90⁰.

Q 3 - In the given figure L₁ || L₂ and ∠A = 65⁰. Then ∠C= ?

q 26

A - 110⁰

B - 115⁰

C - 120⁰

D - 135⁰

Answer : B

Explanation

∠B = ∠A = 65⁰ (corr. ∠s).
∴ ∠B +∠C= 180⁰ ⇒ 65⁰ +∠C = 180⁰ ⇒ ∠C = ( 180⁰ - 65⁰) = 115⁰.

Q 4 - The angles of a triangle are in the ratio 2:3:7. The measure OF the smallest angle is:

A - 90⁰

B - 60⁰

C - 45⁰

D - 30⁰

Answer : D

Explanation

let the angles be (2x)⁰,(3x)⁰ and (7x)⁰. Then,
2x+3x+7x =180 ⇒ 12x =180 ⇒ x=15
Smallest angle = (2x)⁰ = 30⁰

Q 5 - In a ∆ ABC, AB= BC,∠ B= x⁰ and ∠A = (2x-20)⁰. Then, ∠ B= ?

q 34

A - 30⁰

B - 40⁰

C - 44⁰

D - 64⁰

Answer : C

Explanation

AB = BC ⇒ ∠C = ∠A = (2x - 20)⁰. 
∠A+ ∠B + ∠C =180⁰ ⇒ (2x - 20) + x + (2x - 20 ) = 180
⇒ 5x - 40 =180 ⇒ 5x = 220 ⇒ x=44.
∴ ∠B = 44⁰.

Q 6 - If ∆ ABC is an isosceles triangle with ∠ C = 90⁰ and AC = 5cm , Then AB =?

A - 2.5 cm

B - 5 cm

C - 10cm

D - 5√2 cm

Answer : D

Explanation

Clearly BC =AC=5cm.
AB2 = AC2+ BC2 =52 +52= 50 ⇒ AB  = √50 = 5√2 cm.

a 38

Q 7 - A chord of length 30cm is at a distance of 8cm from the center of a circle . The radius of the circle is

A - 11 cm

B - 13 cm

C - 15 cm

D - 17 cm

Answer : D

Explanation

Let O be the centre of the circle and AB  be the chord. Draw OL ⊥  AB.
Then AL= 1/2 AB = (1/2 *30)cm =15 cm  and OL = 8cm.
OA2 = OL2 +AL2= 82 + (15)2  = (64  + 225 ) =289  
⇒ OA = √289  = 17cm.
∴ Radius of the circle is 17 cm.

a 42

Q 8 - In a cyclic quad. ABCD, ∠A=80⁰. Then ∠c =?

q 45

A - 80⁰

B - 160⁰

C - 100⁰

D - 120⁰

Answer : C

Explanation

Opposite angles of a cyclic quadrilateral are supplementary.
∴ ∠A + ∠C = 180 ⁰⇒ 80⁰ + C =180⁰ ⇒ C = 100⁰.

Q 9 - In the given figure, chords AB and CD of a circle intersect externally at P. If AB =6cm, CD = 3cm and PD= 5cm then PB= ?

q 52

A - 5 cm

B - 6.25 cm

C - 6 cm

D - 4 cm

Answer : D

Explanation

PA * PB + PC *PD ⇒ (x+6 ) * x=8* 5 ⇒ x2 +6x - 40 =0
⇒ (x+10) (x-4) =0 ⇒ x=4
∴ PB= 4 cm

Q 10 - In the given figure, measure of ∠ ABC is

q 56

A - 20⁰

B - 40⁰

C - 60⁰

D - 80⁰

Answer : C

Explanation

∠ADC +∠ EDC = 180⁰ ⇒ ∠ADC + 120⁰ = 180⁰ ⇒ ∠ADC= 60⁰
∠ABC = ∠ADC = 60⁰  ( s in the same segment).


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