Question

Note: Figure not drawn to scale

In the circle above, point A is the center and the length of arc BC is 2/5 of the circumference of the circle.
What is the value of x?

Answer 1

The value of x is 144°

Explanation:

Let us revise some facts about the circle

• The measure of the circle is 360°

• The length of the circle is 2πr (circumference)

• If the length of an arc is a/b of the circumference (its length = a/b ×2πr), then the measure of the arc is also a/b of its measure (its measure = a/b × 360°)
• The measure of any central angle equals the measure of its subtended arc

In the given question

∵ A is the center of the circle

∴ Angle x is a central angle subtended by arc BC

∴ The value of x = the measure of arc BC

∵ The length of the arc BC is 2/5 of the circumference of the circle

∴ The measure of arc BC is 2/5 of the measure of the circle

∵ The measure of the circle = 360°

∴ x = 2/5 × 360°

∴ x = 144°

The value of x is 144°