OABCA- 75-B- 90-C- 110-D- 120-

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Angle Sum Property of a Polygon

OABCA. 75∘B. ...

Question

OABC is a rhombus. Find the $∠ A O C .$

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Solution

The correct option is D
OA =AB = BC = OC [Sides of rhombus] ------ (1)
OA = OB = OC [Radii of the circle] ------ (2)
From (1) and (2);
$△$ OAB and $△$ OBC are equilateral triangles.
So, $∠ A O C = ∠ A O B + ∠ C O B$
$∠ A O C = 60^{\circ} + 60^{\circ} = 120^{\circ}$

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Similar questions

In the given figure, the ratio of $∠$ 2 : $∠$ 1 = 2 : 1. Find the value of $∠$ AOB.

Q. In a quadrilateral ABCD, the bisectors of

∠ A

and

∠ B

meet at E. If

∠ C = 75^{\circ}

and

∠ D = 125^{\circ}

, then find the measure of

∠ A E B

The median for the data is

$\begin{matrix} I Q & 60 - 70 & 70 - 80 & 80 - 90 & 90 - 100 & 100 - 110 & 110 - 120 & 120 - 130 N o . o f p u p i l s & 2 & 3 & 5 & 16 & 14 & 13 & 7 \end{matrix}$

The median of the following data is:

$\begin{matrix} I Q & 60 - 70 & 70 - 80 & 80 - 90 & 90 - 100 & 100 - 110 & 110 - 120 & 120 - 130 N o . o f p u p i l s & 2 & 3 & 5 & 16 & 14 & 13 & 7 \end{matrix}$

Q. Question 1
Three angles of a quadrilateral are

75^{\circ}, 90^{\circ} a n d 75^{\circ}

, then the fourth angle is
(a)

90^{\circ}

(b)

95^{\circ}

(c)

105^{\circ}

(d)

120^{\circ}

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OABC is a rhombus. Find the ∠AOC.

The correct option is D OA =AB = BC = OC [Sides of rhombus] ------ (1) OA = OB = OC [Radii of the circle] ------ (2) From (1) and (2); △ OAB and △ OBC are equilateral triangles. So, ∠AOC=∠AOB+∠COB ∠AOC=60∘+60∘=120∘

OABC is a rhombus. Find the $∠ A O C .$

The correct option is D
OA =AB = BC = OC [Sides of rhombus] ------ (1)
OA = OB = OC [Radii of the circle] ------ (2)
From (1) and (2);
$△$ OAB and $△$ OBC are equilateral triangles.
So, $∠ A O C = ∠ A O B + ∠ C O B$
$∠ A O C = 60^{\circ} + 60^{\circ} = 120^{\circ}$