Question

ABC is a triangle inscribed in a circle with center O. If ∠A OC =130° and ∠B OC =150°, find ∠A CB.

Answer 1

65

Explanation:

Recall the arrowhead rule:

Answer 2

65°

Explanation:

Since the triangle ABC is inscribed in a circle with center O, we know that the angles subtended by any chord of the circle are equal. Therefore, we have:

∠AOC = 2∠ACB (angle subtended by chord AC)

∠BOC = 2∠BCA (angle subtended by chord BC)

Substituting the given values, we get:

130° = 2∠ACB

∠ACB = 65°

150° = 2∠BCA

∠BCA = 75°

Finally, we can use the fact that the sum of angles in a triangle is 180° to find ∠CAB:

∠CAB = 180° - ∠ACB - ∠BCA

∠CAB = 180° - 65° - 75°

∠CAB = 40°

Therefore, the measure of ∠ACB is 65°.