Question

In the given figure, O is the centre of the circle. If m(arc AXB) = 80°, then angle AOB =​

Answer 1

AXB = AOB

So 80° = 80°

AOB = 80°

this helpful to you friend

Mark me as a Brainlist

Answer 2

Given:

m(arc AXB) = 80°

To find:

The measure of angle AOB

Solution:

The measure of angle AOB is 80°.

We can find the angle by following the steps given below-

We will take a point C on the major arc and connect it with A and B.

Now, AC and AB meet to form the angle ACB at the circumference of the circle.

We are given that m(arc AXB)=80°.

The measure of the minor arc of the circle i.e., arc AXB is twice the angle formed by A and B on the major arc of the circle.

So, m(arc AXB)=2×m(angle ACB)

On putting the values, we get

80°=2×m(angle ACB)

80/2=m(angle ACB)

Angle ACB=40°

Now, we know that the angle subtended by A and B on the circumference of the circle is half the angle made by A and B at the centre of the circle.

Angle ACB=1/2 of angle AOB

We will substitute the value of the angle ACB,

40°=1/2 of angle AOB

40×2=angle AOB

80°=Angle AOB

Therefore, the measure of angle AOB is 80°.