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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?
Answer : C
Explanation
∠ROQ = ∠POS (vert. opp. ∠s) = 90⁰.
Answer : A
Explanation
x+y = 180 ⇒ x+ 4/5 x = 180 ⇒ 5x +4x = 900 ⇒ 9x=900 ⇒ x = 100.
Q 3 - If OE is the bisector of ∠AOD in the given figure ,then the value of X and y are respectively
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 - The angles of a triangle are in the ratio 2:3:7. The measure OF the smallest angle is:
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 - The angle of a triangle are 3x⁰, (2x-7)⁰ and (4x-11)⁰. The value of x is :
Answer : A
Explanation
The sum of the angle of a triangle is 180⁰. ∴ 3x = 2x - 7 + 4x -11 = 180 ⇒ 9x =162 ⇒ x = 18. Hence, x = 18.
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
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.
Q 8 - In the given figure ,ABCD is a cyclic quadrilateral in which AB || DC and ∠ BAD = 100⁰. Then , ∠ ABC=?
Answer : B
Explanation
AB DC and AD is the transversal. ∴ ∠ADC + ∠DAB=180⁰ ⇒ ADC =100⁰ =180⁰ ⇒ ADC=80⁰. Opposite angles of a cyclic quadrilateral are supplementary. ∴ ∠ADC +∠ABC = 180⁰ ⇒ 80⁰+ ∠ABC =180⁰ ⇒ ABC = 100⁰.
Q 9 - In the given figure, AOB is a diameter of the circle and CD || AB. If ∠DAB = 25⁰ ,Then ∠CAD=?
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
Answer : C
Explanation
∠ADC +∠ EDC = 180⁰ ⇒ ∠ADC + 120⁰ = 180⁰ ⇒ ∠ADC= 60⁰ ∠ABC = ∠ADC = 60⁰ ( s in the same segment).