Question

In the figure. O is the centre of the circle Angle OAD is 48º and OCD = 31⁰ What is the measure of AOC?​

Answer 1

Answer:

79º

Step-by-step explanation:

it is ok

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Answer 2

The $\bf \angle AOC={158}^{\circ}$

Given:

• O is the centre of the circle.
• $\angle OAD={48}^{\circ}$ and $\angle OCD={31}^{\circ}$.

To find:

• What is the measure of $\angle AOC$?

Solution:

Theorem to be used:

1. If two sides of a triangle are equal than angles opposite to equal sides are equal.
2. Sum of all interior angles of a triangle is 180°.
3. A complete angle around a point is 360°.

Step 1:

Find $\angle ADO$.

Construct OD.

It will create two triangles; ∆ADO and ∆CDO.

Because

OD=OA [Radius]

Thus,

According to the theorem,

$\angle OAD=\angle ADO$

$\bf \angle ADO={48}^{\circ}$.

Step 2:

Find $\angle AOD$.

In ∆ADO

$\angle OAD+\angle ADO+\angle AOD=180^{\circ}$

or

$\angle AOD=180^{\circ}-{48}^{\circ}-{48}^{\circ}$

or

$\bf \angle AOD=84^{\circ}$

By the same way find angles $\angle COD$

and $\angle CDO$ in ∆CDO.

$\bf \angle CDO=31^{\circ}$

and

$\bf \angle COD=118^{\circ}$

Step 3:

Find $\angle AOC$

$\angle AOC+\angle COD +\angle AOD=360^{\circ}$

$\angle AOC+118^{\circ}+84^{\circ}=360^{\circ}$

or

$\bf \red{\angle AOC=158^{\circ}}$

Remark: This can be done by theorem which states that, Angle subtended by arc at corresponding segment of circles doubles at the center.

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