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2. Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. (4 points) Show your work. (1 point)

m∠A = 91°

m∠B = 146°

m∠C = 89°

m∠D = 34°

Step-by-step explanation:

If the four vertices of a quadrilateral lie on the edge of a circle, then this quadrilateral is called cyclic quadrilateralIn the cyclic quadrilateral each two opposite angles are supplementary (means the sum of their measures is 180°)The sum of the measures of the interior angles of any quadrilateral is 360°

In quadrilateral ABCD

∵ A, B, C, And D lie on the circumference of the circle

∴ ABCD is a cyclic quadrilateral

∴ The sum of the measures of each opposite angles is 180°

∵ ∠A and ∠C are opposite angle in the cyclic quadrilateral ABCD

∴ m∠A + m∠C = 180°

∵ m∠A = (2x + 3)°

∵ m∠C = (2x + 1)°

- Add them and equate the answer by 180

∴ (2x + 3) + (2x + 1) = 180

- Add the like terms in the left hand side

∴ 4x + 4 = 180

- Subtract 4 from both sides

∴ 4x = 176

- Divide both sides by 4

∴ x = 44

Substitute the value of x in the expressions of angle A, C, D

∵ m∠A = 2(44) + 3 = 88 + 3

∴ m∠A = 91°

∵ m∠C = 2(44) + 1 = 88 + 1

∴ m∠C = 89°

∵ m∠D = x - 10

∴ m∠D = 44 - 10

∴ m∠D = 34°

- ∠B and ∠D are opposite angles in the cyclic quadrilateral ABCD

∴ m∠B + m∠D = 180°

∴ m∠B + 34 = 180

- Subtract 34 from both sides

∴ m∠B = 146°

its a and d

Step-by-step explanation: