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Class 9 Exam  >  Class 9 Tests  >  Test: Angle Relations In Parallelogram - Class 9 MCQ

Test: Angle Relations In Parallelogram - Class 9 MCQ


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15 Questions MCQ Test - Test: Angle Relations In Parallelogram

Test: Angle Relations In Parallelogram for Class 9 2024 is part of Class 9 preparation. The Test: Angle Relations In Parallelogram questions and answers have been prepared according to the Class 9 exam syllabus.The Test: Angle Relations In Parallelogram MCQs are made for Class 9 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Angle Relations In Parallelogram below.
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Test: Angle Relations In Parallelogram - Question 1
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The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If ∠DAC = 32°, ∠AOB = 70°, then ∠DBC is equal to:

Detailed Solution for Test: Angle Relations In Parallelogram - Question 1

Answer:

<DBC = 38°

Step-by-step explanation:

Given:

ABCD is a parallelogram .

AC,BD diagonals intersecting at "O".

<DAC = 32°, <AOB = 70°

Proof:

i) AB//DC , AC is a transversal.

<DAC = <BCA = 32°

/* Alternate angles */

ii) In ∆BCO , CO extended to A.

Sum of interior opposite angles = Exterior angle at O

=> <BCA + <OBC = <AOB

=> <BCA + <DBC = <AOB

=> 32° + <DBC = 70°

=> <DBC = 70°-32°

=> <DBC = 38°

Test: Angle Relations In Parallelogram - Question 2
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The opposite angles of a parallelogram are (3x – 2)° and (50 – x)° the measure of these angles is ______.​

Detailed Solution for Test: Angle Relations In Parallelogram - Question 2

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Test: Angle Relations In Parallelogram - Question 3
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In parallelogram ABCD, if ∠A = 2x + 15°, ∠B = 3x – 25°, then value of x is:

Detailed Solution for Test: Angle Relations In Parallelogram - Question 3

2x+15+3x-25=180
[co interior angles]
5x-10=180
5x=190
x=38
option d is right answer

Test: Angle Relations In Parallelogram - Question 4
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In a parallelogram the sum of two consecutive angles is
Test: Angle Relations In Parallelogram - Question 5
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Bisectors of angles of a parallelogram form a
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Test: Angle Relations In Parallelogram - Question 6
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ABCD is a parallelogram in which ∠DAB = 75° and ∠DBC = 60°, the measure of ∠CDB and ∠ADB is
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Test: Angle Relations In Parallelogram - Question 7
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In a parallelogram PQRS, if diagonal PR bisects the ∠P, then it also bisects _____.
Test: Angle Relations In Parallelogram - Question 8
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ABCD is a parallelogram in which the bisectors of angles ∠A and ∠B intersect at point P then ∠APB is
Detailed Solution for Test: Angle Relations In Parallelogram - Question 8

Since ABCD is a Parallelogram. Therefore,
AD || BC
AB is a transversal . Therefore ,

A + B = 180°. [ Consecutive interior angles]

Multiply both sides by 1/2 ,

1/2 A + 1/2 B = 1/2 (180°)
1/2 A + 1/2 B = 90° __【1】

Since, AP and PB are angle bisectors of A and B . Therefore,

Angle 1 = 1/2 A
Angle 2 = 1/2 B

Substitute the values in【1】,

Angle 1 + Angle 2 = 90°____【2】

Now, in ∆ APB,
1 + APB + 2 = 180°
90° + APB = 180°. [From 【2】]
APB = 90°
- HENCE PROVED

Test: Angle Relations In Parallelogram - Question 9
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One angle of a parallelogram is 30° less than twice the smallest angle then the measure of each angle of the parallelogram is
Test: Angle Relations In Parallelogram - Question 10
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Perimeter of a parallelogram is 22 cm. If the longer side, measures 6.5 cm, the measure of the shorter side will be
Test: Angle Relations In Parallelogram - Question 11
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If PQRS is a parallelogram, then ∠Q – ∠S is equal to:
Test: Angle Relations In Parallelogram - Question 12
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The diagonals of a rectangle PQRS intersects at O. If ∠QOR = 44°, ∠OPS =?
Detailed Solution for Test: Angle Relations In Parallelogram - Question 12

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Test: Angle Relations In Parallelogram - Question 13
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In the given figure, PQRS is a parallelogram and ∠R is 100° then ∠Q is
Test: Angle Relations In Parallelogram - Question 14
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In a parallelogram ABCD, if ∠A = 75°, then ∠B = ?
Test: Angle Relations In Parallelogram - Question 15
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AN and CP are perpendiculars to the diagonal BD of a parallelogram ABCD. Choose the correct option
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