Answer:
The value of x is 13
Step-by-step explanation:
* Lets study the to circles
- The are congruent
- The length of chord TS equal to the length of chord UV
- The measure of the minor arc TS equal to the measure
of minor arc UV
- The measure of the major arc TS equal to the measure
of major arc UV
* We now that the measure of any circle = 360°
∴ The sum of the measure of the minor arc and the measure
of the major arc equal to 360°
* In circle Q:
∵ The measure of the major arc UV is 22x - 13°
∵ The measure of the minor arc UV is 10x - 43° ⇒ circle R ≅ circle Q
∵ The sum of the measure of the two arcs = 360°
∴ 22x - 13 + 10x - 43 = 360 ⇒ add the like terms
∴ 32x - 56 = 360 ⇒ add 56 to both sides
∴ 32x = 416 ⇒ divide both sides by 32
∴ x = 13
* The value of x is 13
