A circular arc AC that does not contain point B is 165 degrees and a circular arc BC

A circular arc AC that does not contain point B is 165 degrees and a circular arc BC that does not contain point A is 55 degrees. Find the inscribed angle ACB.

Let’s start with the fact that we can find an arc of a circle AB, which does not contain point C. To do this, we need to add up the data we know and subtract it from 360 °. We get: 360 – (165 + 55) = 140 °.

We also know that the inscribed angle ACB resting on the arc AB, which does not contain the point C, is equal to half the degree measure of this arc.

From this follows 140 ° / 2 = 70 °.

Answer: 70 °.