Question

(ii) Measure of 4 ACB is equal to (a) 45* (b) 60° (c) 30° (d) 90°​

Answer 1

Answer:

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Step-by-step explanation:

>>Maths

>>Circles

>>Angles in the Same Segment

>>In Fig 10.9 AOB = 90^∘ and ABC = 30^∘

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In Fig 10.9 ∠AOB=90

∘

and∠ABC=30

∘

then∠CAO is equal to

426581

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Easy

Solution

Correct option is D)

In △AOB

OA=OB

∴∠OAB+∠OBA+∠AOB=180

0

=>2∠OAB+90

0

=180

0

=>2∠OAB=180

0

−90

0

=90

0

=>∠OAB=

2

90

=45

0

We know that the angle subtended at the centre of the circle by an arch is twice the angle subtended at the circumference by the same arc.

∴∠ACB=

2

1

∠AOB

=

2

90

=45

0

Again in △ABC

∠ACB+∠CBA+∠BAC=180

0

=>45

0

+30

0

+∠BAC=180

0

=>∠BAC=180

0

1. 75

0

=105

0

∴∠CAO=∠BAC−∠OAB

=>∠CAO=105

0

−45

0

=60

0