Question

Can u solve this for me thank u

Answer 1

Part (A) → x = 5

Part (B) → m(arc RS) = 55°

Explanation:

In the picture attached,

RU and SV are the diameters of the given circle.

Part (A),

Since RU is the diameter,

m(arc RVU) = 180°

m(arc RV) + m(arc VU) = 180°

(24x + 5) + (10x + 5) = 180

34x + 10 = 180

34x = 170

x =
`(170)/(34)`

x = 5

Part (B),

Since m(arc RS) = m(arc VU) [Angles intercepted by these arcs at the center are equal because they are the vertical angles]

m(arc RS) = (10x + 5)

= (10×5 + 5)

= 55°