Question

In the given figure, ABCD is a rectangle, diagonals AC and BD intersect at O
and Angle AOB= 60°. Find the measure of Angle OAD.

Someone Pl. answer Quickly. i will mark as the brainliest​

Answer 1

Answer:

60

Step-by-step explanation:

angle AOB = OAD

opposite angles are equal in rectangular

so,angle=60 degree

Answer 2

Given:

Angle AOB= 60°

To find:

The measure of Angle OAD

Solution:

The measure of Angle OAD is 30°.

We can find the angle by following the given steps-

We know that the diagonals of a rectangle are of equal length.

So, in rectangle ABCD, AC and BD are equal and divide each other into two equal parts.

Since AC and BD intersect at O, the length of AO and BO is equal.

Angle OBA=Angle OAB (Angles opposite to equal sides)

Now, in ΔAOB, the sum of all angles is 180°.

So, angle AOB+angle OBA+ angle OAB=180°

We are given that angle AOB=60°

60°+angle OAB+ angle OAB=180°

2(angle OAB)=180°-60°

2(angle OAB)=120°

Angle OAB=60°

So, angle OAB=angle OBA=60°

We know that all the angles of a rectangle are right angles.

Angle A=90°

Angle A=Angle OAB+Angle OAD

Using the values,

90°=60°+angle OAD

90°-60°=Angle OAD
Angle OAD=30°

Therefore, the measure of Angle OAD is 30°.