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The values of x and y are x = 95 and y = 25

Step-by-step explanation:

If a quadrilateral is inscribed in a circle which means all its vertices lie on the circumference of the circle, then it is called a cyclic quadrilateral.

The properties of the cyclic quadrilateral

In the given figure

∵ The four vertices of the quadrilateral QRTU lie on the circle

∴ QRTU is a cyclic quadrilateral

∵ ∠ PQU is an exterior angle of quadrilateral QRTU at Q

∵ ∠RTU is the opposite interior angle to it

→ By using the 2nd property above

∴ m∠PQU = m∠RTU

∵ m∠PQU = 95°

∵ m∠RTU = x°

∴ x = 95

∵ ∠QRT and ∠QUT are opposite angles in the cyclic quadrilateral

→ By using the 1st property above

∴ m∠QRT + m∠QUT = 180° ⇒ supplementary angles

∵ m∠QRT = 110°

∴ 110 + m∠QUT = 180°

→ Subtract 110 from both sides

∴ m∠QUT = 70°

In ΔSQU

∵ ∠ PQU is an exterior angle to the Δ T vertex Q

→ That means its measure equal the sum of the measures of the

   two opposite interior angles QSU and QUS

∴ m∠PQU = m∠QSU + m∠QUS

∵ m∠PQU = 95°

∵ m∠QSU = y°

∵ m∠QUS = 70°

∴ 95 = y + 70

→ Subtract 70 from both sides

∴ 25 = y

∴ y = 25

56

step-by-step explanation:

the answer is a

step-by-step explanation: