What is the value of - ACB- if - OAB-20- -70

The correct option is A 70In the figure, ∠ OAB=20^∘. As OAB is an isosceles triangle, ∠ OAB=∠ OBA=20^∘. Now, ∠ OAB+∠ OBA+∠ AOB=180^∘ 20^∘+20^∘+∠ AOB=180^∘ ∠ A ...

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Standard IX

Mathematics

Construction of Circle Segment

What is the v...

Question

What is the value of $∠ A C B$ , if $∠ O A B = 20^{\circ}$ ?
70

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Solution

The correct option is A 70
In the figure, $∠ O A B = 20^{\circ}$ .
As $△ O A B$ is an isosceles triangle, $∠ O A B = ∠ O B A = 20^{\circ} .$

Now, $∠ O A B + ∠ O B A + ∠ A O B = 180^{\circ} 20^{\circ} + 20^{\circ} + ∠ A O B = 180^{\circ} ∠ A O B = 180^{\circ} - 40^{\circ} ∠ A O B = 140^{\circ}$

Also, $∠ A C B = \frac{1}{2} ∠ A O B ∠ A C B = \frac{1}{2} \times 140^{\circ} ∠ A C B = 70^{\circ}$

Hence, the value of $∠ A C B$ is $70^{\circ}$ .

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Similar questions

Q. In the given figure, O is the centre of a circle. If ∠OAB = 40°, then ∠ACB = ?
(a) 40°
(b) 50°
(c) 60°
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What is the value of ∠ACB, if ∠OAB=20∘ ?70

The correct option is A 70In the figure, ∠OAB=20∘. As △OAB is an isosceles triangle, ∠OAB=∠OBA=20∘. Now, ∠OAB+∠OBA+∠AOB=180∘20∘+20∘+∠AOB=180∘∠AOB=180∘−40∘∠AOB=140∘ Also, ∠ACB=12∠AOB∠ACB=12×140∘∠ACB=70∘ Hence, the value of ∠ACB is 70∘.

What is the value of $∠ A C B$ , if $∠ O A B = 20^{\circ}$ ?
70