Congruent Triangles std8 Page-35.3 EM

⚪ Circle Geometry | Central Angles | Triangle ABC

Center O | Points A (apex), C (right), B (bottom) | ∠AOB = 110°, ∠AOC = 120°

⚪ Circle with center O 📐 ∠AOB = 110° 📐 ∠AOC = 120° 🟢 Triangle ABC (green) is inscribed

✍️ Find the third central angle and all angles of triangle ABC

1 Central angles around point O

What is the total measure of angles around point O?

2 Calculate ∠BOC

∠AOB = 110°, ∠AOC = 120°. Find ∠BOC.

3 Inscribed angle theorem

The measure of an inscribed angle is _____ the measure of its intercepted arc (central angle).

4 Find ∠ACB

∠ACB subtends arc AB. Central angle AOB = 110°. ∠ACB = ?

5 Find ∠ABC

∠ABC subtends arc AC. Central angle AOC = 120°. ∠ABC = ?

6 Find ∠BAC

∠BAC subtends arc BC. Central angle BOC = 130°. ∠BAC = ?

7 Verify triangle angle sum

Check: ∠BAC + ∠ABC + ∠ACB = 65° + 60° + 55° = ?

8 Final answer - Central angles

The three central angles are:

9 Final answer - Triangle ABC angles

The angles of triangle ABC are:

10 Complete the statement

The third central angle ∠BOC = _____