Question

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Answer 1

Given:

In circle D, the measure of angle ADC is 108 degrees.

To find:

The measure of angle ABC.

Solution:

Central angle theorem: According to this theorem, the measure of central angle of an arc is twice of the measure of inscribed angle on that arc.

Using the Central angle theorem, we get

$m\angle ADC=2\times m\angle ABC$

$108^\circ=2\times m\angle ABC$

$\dfrac{108^\circ}{2}= m\angle ABC$

$54^\circ= m\angle ABC$

Therefore, the measure of angle ABC is 54 degrees.