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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, straight line AB and CD intersect at O. IF ∠δ =3∠v, then ∠v = ?

q 18

Answer : B

Explanation

COD is a  straight line 
∴ ∠δ + ∠v =180⁰ ⇒ 3v +v =180 ⇒ 4v = 180 ⇒ v =45⁰.

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 the given figure , AB ll CD, ∠ABE =120⁰, ∠DCE = 100⁰ and ∠BEC =x⁰. Then, x= ?

q 29

Answer : C

Explanation

Through E draw GEH ∥ AB ∥CD
AB∥ EG and BE is the transversal.
∠ ABE +∠ GEB = 180⁰ ⇒ 120⁰ +∠GEB =180⁰ ⇒ ∠GEB = 60⁰
CD ∥EH and CE is the transversal. 
∴∠DCE +∠CEH = 180⁰  ⇒ 100⁰ + ∠CEH =180⁰  ⇒ CEH = 80⁰
NOW ∠GEB+ ∠BEC +∠CEH = 180⁰ ⇒ 60+x+80 =180 ⇒ x = 40

a 29

Q 5 - In A ∆ABC ,∠A-∠B=33⁰ and∠ B -∠C = 18⁰ . Then∠ B =?

Answer : B

Explanation

∠ A- ∠B = 33⁰ and ∠B -∠C =18⁰
⇒ A= 33+ B and C=B -18
= (33+B) + B + (B-18) =180
⇒ 3B =165 ⇒ B 55.
 ∴  ∠B =55⁰.

Q 6 - A ladder is placed in such a way that its foot is 15m away from a wall and its top reaches a window 20m above the ground. The length of the ladder is:

Answer : C

Explanation

Let BC be the wall and AB be the ladder.
Then , BC = 20 m and AC =15m
∴ AB²= BC² +AC² = (20)² + (15)² = (400 + 225) = 625
⇒ AB = √625 = 25m.

a 40

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 a cyclic quad. ABCD, ∠A=80⁰. Then ∠c =?

q 45

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

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

Answer : C

Explanation

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

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