Answer:
The values of x and y are x = 25 and y = 18
Step-by-step explanation:
The measure of an arc is equal to the measure of the central angle subtended by it
In circle W
∵ W is the center of the circle
∵ m∠QWS = 90°
∵ ∠QWS is subtended by arc QS
- Use the rule above
∴ m∠QWS = m arc QS
∴ m arc QS = 90°
∵ m arc QS = m arc QR + m arc RS
∵ m arc QR = (x + 11)°
∵ m arc RS = (3y)°
- Add them and equate the answer by 90
∴ (x + 11) + (3y) = 90
- Subtract 11 from both sides
∴ x + 3y = 79 ⇒ (1)
∵ VT passes through W
∴ VT is a diameter in circle W
- Diameter divides the circle into two equal arcs the measure
of its arc is 180° because the measure of the circle is 360°
∴ m arc VQRST is 180°
∵ m arc QRS = 90°
∵ m arc VQRST = m arc VQ + m arc QRS + m arc ST
- Substitute the measures of arc VQRST and QRS
∴ 180 = m arc VQ + 90 + m arc ST
- Subtract 90 from both sides
∴ 90 = m arc VQ + m arc ST
∵ m arc VQ = (y + 7)°
∵ m arc ST = 65°
∴ 90 = (y + 7) + 65
- Add like terms in the right hand side
∴ 90 = y + 72
- Subtract 72 from both sides
∴ 18 = y
Substitute the value of y in equation (1) to find x
∵ x + 3(18) = 79
∴ x + 54 = 79
- Subtract 54 from both sides
∴ x = 25
The values of x and y are x = 25 and y = 18
