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?

Question

asked Sep 17, 2021 105k views

2 Answers

Yly · Answer 1 · 2021-09-20T21:14:23+0000

Answer:

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°.