Question

A circle is centered on point BBB. Points AAA, CCC and DDD lie on its circumference.

If \blue{\angle ABC}∠ABCstart color #6495ed, angle, A, B, C, end color #6495ed measures 124^\circ124

∘

124, degrees, what does \orange{\angle ADC}∠ADCstart color #ffa500, angle, A, D, C, end color #ffa500 measure?

Answer 1

The real answer is 20 its not that high of a number

Explanation:

Answer 2

`\angle ADC=62^\circ`

Explanation:

Given the circle centered on point B with points A, C and D on its circumference.

`\angle ABC` is the angle subtended by arc AC at the centre.

Since D is on the circumference,
`\angle ADC` is the angle subtended by arc AC on the circumference.

Circle Theorem: The measure of the angle subtended by an arc at the center is twice the measure of the angle subtended by same arc at the circumference.

By the theorem stated above:

`\angle ABC = 2 X \angle ADC\\Since \angle ABC=124^\circ\\124^\circ = 2 X \angle ADC\\ \angle ADC=124^\circ / 2\\\\ \angle ADC=62^\circ`