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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.

Q 1 - In the given figure , ∠POS = 90⁰. What Is the measure of ∠ROQ?

q 19

Answer : C

Explanation

∠ROQ = ∠POS (vert. opp. ∠s) = 90⁰.

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

Answer : A

Explanation

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

Q 3 - In the given figure , AB || CD, ∠ABE =35⁰, ∠CDE = 65⁰ and ∠BED =x⁰. Then, x= ?

q 27

Answer : B

Explanation

Draw GEH ||AB||CD.
∠ BHE =∠ ABE = 35⁰ (alt .∠s)
∠ DEH =∠ CDE = 65⁰ (alt .∠s)
∴∠x=∠ BEH + ∠DEH = (35⁰ +65⁰)=100⁰.

a 27

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

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 - ∆ABC is right angled at A. If AB =24 mm and AC =7mm, BC=?

Answer : B

Explanation

By Pythagoras  theorem , we have 
 BC² = AB² + AC²    
= (24)²  + 7²
= 576 + 49 = √625 ⇒ BC = 625 = 25mm.

Q 6 - Two poles of heights 6m and 11m stand vertically on a plane ground. If the distance between their feet is 12m , what is the distance between their tops?

Answer : A

Explanation

Let AB and CD be the poles such that
 AB = 6m , CD = 11 m and BD =12m 
Draw AE ⊥ CD . Then , AE = BD = 12m
CE = CD - DE = CD - AB = (11 - 6) m =5m.
from right   AEC we have
AC² = AE²  + CE² = (12)² + 5² = (114 +25)=169
⇒ Ac =  √169 = 13m
∴ Distance between their tops= 13m

a 39

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

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 the given figure , O is the center of a circle and arc ABC subtends an angle of 130⁰ at O. AB is extended to P. Then ∠PBC= ?

q 48

Answer : C

Explanation

Take a point D on the remaining part of circumference of the circle. Join DA and DC
 ∠ADC = 1/2  ∠AOC = 1/2 *130⁰ = 65⁰.
Now DABC is a cyclic quadrilateral. 
&There4; ∠ADC + ∠ABC = 180⁰⇒ 65⁰+ ∠ABC = 180⁰ ⇒ ∠ABC = 115⁰.
⇒∠ PBC= (180⁰ - 115⁰) =65⁰.

Q 9 - In the given fig. PAB is a secant and PT is a tangent to the circle from P. If PT = 4cm and AB = xcm , Then PB = ?

q 51

Answer : C

Explanation

PA *PB = PT² ⇒ 4*(4+x)=25 ⇒ 4=x = 25/4 = 6.25 ⇒ x= 2.25 cm.

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

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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