Calculate the measure of - AOC- 120-70-140-90-

The correct option is C 140^∘ Join AC. In Δ AOB, OA = OB (radii of same circle) ∠ OAB = ∠ OBA = 40^∘ In Δ OBC, OC = OB (radii of same circle) ∠ OCB = ∠ OBC = ...

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Standard X

Mathematics

Angles Subtended by an Arc at the Centre Is Twice the Angle Subtended at the Circumference

Calculate the...

Question

Calculate the measure of $∠ A O C .$

$120^{\circ}$

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$70^{\circ}$

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$140^{\circ}$

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$90^{\circ}$

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Solution

The correct option is C
$140^{\circ}$

Join AC.
In $Δ A O B,$

OA = OB (radii of same circle)

$∠ O A B = ∠ O B A = 40^{\circ}$

In $Δ O B C$ ,

OC = OB (radii of same circle)

$∠ O C B = ∠ O B C = 30^{\circ}$

Now,

$∠ A B C = ∠ A B D + ∠ O B C$

$= 40 + 30 = 70^{\circ}$

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

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Similar questions

Q. In Fig. 104, AB || CO, ∠OAB = 150° and ∠OCO = 120°. Then, ∠AOC =
(a) 80°
(b) 90°
(c) 70°
(d) 100°

The table given here shows the number of calories contained in one serving of student's favourite cereals.

Number of calories per serving of cereals

$70$	$120$	$100$	$100$	$140$
$70$	$120$	$100$	$100$	$100$
$110$	$100$	$110$	$120$	$100$
$110$	$100$	$100$	$110$	$150$
$90$	$110$	$120$	$110$	$100$
$140$	$130$	$100$	$80$	$100$
$100$	$110$	$80$	$90$	$110$

How many calories are in one serving of most of the cereals?

Mark (✓) against the correct answer
In the given figure, AB || CD. ∠OAB = 150° and ∠OCD = 120°.
Then ∠AOC = ?

(a) 80°
(b) 90°
(c) 70°
(d) 100°

The measure of $∠ A O C =$ ___

Measure of the four angles ∠A, ∠B, ∠C and ∠D in the given parallelogram will be

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Calculate the measure of ∠AOC.

The correct option is C 140∘ Join AC. In ΔAOB, OA = OB (radii of same circle) ∠OAB=∠OBA=40∘ In ΔOBC, OC = OB (radii of same circle) ∠OCB=∠OBC=30∘ Now, ∠ABC=∠ABD+∠OBC =40+30=70∘ ∠AOC=2∠ABC=2×70=140∘

Calculate the measure of $∠ A O C .$