Mathematics 10 — Exercise 8.2 · Q2

Full question

Marked chords AB=BC=CD; angle AOC=154°, arc AB=3 cm. Find x=angle DOC and y=arc DCB.

Step-by-step solution

1. AB,BC,CD are marked equal, so their central angles AOB,BOC,COD are equal.

2. Angle AOC=154° contains two of those equal angles: 2x=154°.

   $$2\times x=154$$

3. Divide by 2: x=77°.

   $$x=77$$

4. Equal chords have equal corresponding minor arcs. Arc AB=3 cm gives BC=3 cm and CD=3 cm.

5. The labelled y is arc DCB, comprising DC and CB. Add 3+3.

   $$y=3+3$$

6. Therefore y=6 cm.

   $$y=6$$

Answer

The final answer is shown below.