Question

Can somebody help me this is my last one

Answer 1

The value of x is 13

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