Question

I need help finding the measurement of angle C

Answer 1

110
48
180
77

Answer 2

I'm not exactly sure, I wonder if this is consistent.

I made some assumption that when a triangle intersects with a circle on every 3 points, the outer rotation is something 180 deg instead of 360, because i would think that every arc line that seems like it "zoomed out" of the angle is identical in angle. Hope I get corrected if I'm wrong, it's not even in the answers, anyway.

Answer 3

The circle still has 360°.
The vertex of the angles in on the circle, so the arcs are twice the measure of the angle.

Answer 4

Then use the fact that the angles in a triangle add up to 180° to find angle C

Answer 5

@TangerineSkyys

Angles A, C, and B are inscribed angles of the circle and have measure 1/2 the intercepted arc.

Arc CB is 96 because <A = 48.
Arc AC is given to be 100.

Arc CB + Arc AC + Arc AB = 360
96 + 110 + Arc AB = 360
Arc AB = 154.

Arc AB is the arc intercepted by inscribed angle C.

Angle C has measure 1/2 * 154 = 77 degrees