Question

A circle is centered on point B. Points A, C and D lie on its circumference.

If angle ADC measures 35, what does angle ABC measure?

Answer 1

Explanation:

70

Answer 2

The angle ABC is 70°.

Explanation:

You can observe a representation of the problem in the image attached.

According to the inscribed angle theorem, the angle created by two chords is half of its subtended arc, that means

`\angle ADC = (1)/(2)(AC)\\ 35\°=(1)/(2) (AC)\\AC=70\°`

Now, observe that the arc AC has as central angle the angle ABC, according to the theorem, the subtended arc and its central are congruent.

`\angle ABC \cong arc(AC)`

Therefore, the angle ABC is 70°.