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

Answer:

The angle ABC is 70°.

Step-by-step 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

$\angle ADC = \frac{1}{2}(AC)\\ 35\°=\frac{1}{2} (AC)\\AC=70\°$

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°.

Answer 2

Answer:

Step-by-step explanation:

70