Answer:
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°