Geometry - Online Quiz

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 - The sum of all angles around a point is

A - 0⁰

B - 90⁰

C - 180⁰

D - 360⁰

Answer : D

Explanation

The sum of all angle around a point is 360⁰ .

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 - If OE is the bisector of ∠AOD in the given figure ,then the value of X and y are respectively

q 25

A - 45⁰, 45⁰

B - 66⁰, 48⁰

C - 48⁰ ,66⁰

D - 30⁰, 60⁰

Answer : B

Explanation

∠AOC is a straight angle.
∴ 132⁰ + y⁰ = 180⁰ ⇒ y = (180 -  132 ) = 48⁰.
∠AOC = ∠BOC (vert. opp. ∠s) = 132⁰
∴ x= 1/2 ∠AOD = 1/2 * 132⁰ = 66⁰
∴ x= 66 and y = 48.

Q 4 - In a ∆ ABC, if 2∠A =3∠B =6∠C, Then ∠B= ?

A - 30⁰

B - 90⁰

C - 60⁰

D - 45⁰

Answer : C

Explanation

let 2∠ A = 3∠B = 6∠ C=ℏ. Then  ∠A = ℏ/2 , ∠ B = ℏ/3 and ∠ C =ℏ/6
But , ∠ A+∠B+∠C = 180⁰
∴  ℏ/2 + ℏ/3+ ℏ/6 = 180 ⇒ 3 ℏ+2 ℏ+ ℏ = 180*6 ⇒ 6 ℏ =180*6 ⇒ ℏ=180    ⇒ ∠B = 180/3 =60⁰

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 - The radius of a circle is 13cm and AB is a chord which is at a distance of 12cm from the center. The length of the ladder is:

A - 35 cm

B - 17.5 cm

C - 25 cm

D - 10 cm

Answer : D

Explanation

Let O be the  center of the circle and AB be the chord . Form  O, draw OL ⊥ AB. join OA.
Then, oA = 13 cm and OL = 12cm.
∴ AL2 = OA2 -OL2=(13)2 - (12)2= (169-144) =25.
=.> AL= √25 =5 cm
⇒ AB = 2 * AL =(2*5) cm = 10 cm.

a 41

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, AOB is a diameter of the circle and CD || AB. If ∠DAB = 25⁰ ,Then ∠CAD=?

q 49

A - 45⁰

B - 40⁰

C - 65⁰

D - 115⁰

Answer : B

Explanation

AB  DC and AC is a transversal.
∴ ∠ACD = ∠CAB = 25⁰ (alt. s )
∠ACB = 90⁰ ( angle in a semicircle)
∴ ∠BCD =∠ACB + ∠ ACD=(90⁰ +25⁰)= 115⁰.
∠BAD + ∠BCD = 180⁰ ⇒ ∠BAC +∠CAD +∠BCD = 180⁰
⇒ 25⁰ +∠ CAD + 115⁰ =180⁰ ⇒ ∠CAD = 40⁰

Q 10 - In The adjoining figure, ABCD is a rhombus whose diagonals intersect at O. IF ∠OAB =40⁰ and ∠ABO =x⁰, then X= ?

q 54

A - 50⁰

B - 35⁰

C - 40⁰

D - 45⁰

Answer : A

Explanation

We know that the diagonals of a  rhombus
bisect each other at right angle . So ,∠ AOB = 90⁰. 
Now ,∠ OAB + ∠ABO + ∠AOB = 180⁰
⇒ 40 +x + 90 = 180 ⇒ x=50.

a 54

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