Question

in the given figure , A , B , C , D are points on a circle such that angle ACB = 40 degree nd angle DAB = 60 degree the measure of angle DBA is

Answer 1

Answer:

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Answer 2

Given:

Angle ACB=40°

Angle DAB=60°

To find:

The measure of angle DBA

Solution:

The measure of angle DBA is 80°.

We can find the angle by following the given process-

We know that the angles in the same segment of the circle, formed by the same chord are equal.

Chord AB forms the two angles, angle ADB and angle ACB.

We are given that angle ACB=40° and angle DAB=60°.

So, angle ADB=angle ACB=40°

Now, in ΔDAB,

Angle DAB=60°

Angle ADB=40° (angles formed in the same segment)

Let the angle DBA be X.

The sum of all angles in ΔDAB is 180°.

So, angle DAB+angle ADB+ angle DBA=180°

On putting the values,

60°+40°+X=180°

100°+X=180°

X=180°-100°

X=80°

Therefore, the measure of angle DBA is 80°.