If mVQ=(y+7), mQR=(x+11), mRS=(3y),and mST=65,findthevaluesofxandy

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

283 square feet

step-by-step explanation:

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