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

For some reason the picture changed when I uploaded it but

A is (2x + 3)

B doesn't have a answer because we're supposed to find that

C is (2x + 1)

D is is the same as the picture which is (x - 10)

The measure of the angles are ∠A = 91°, ∠C = 89° and ∠D = 34°

Explanation:

Given that the quadrilateral ABCD is inscribed in a circle.

The given angles are ∠A = (2x + 3), ∠C  = (2x + 1) and ∠D = (x - 10)

We need to determine the measures of the angles A, C and D

The value of x:

We know that, the opposite angles of a cyclic quadrilateral add up to 180°

Thus, we have,

Substituting the values, we have,

Thus, the value of x is 44.

Measure of ∠A:

Substituting in ∠A = (2x + 3)°, we get,

Thus, the measure of angle A is 91°.

Measure of ∠C :

Substituting in ∠C = (2x + 1)°, we get,

Thus, the measure of angle C is 89°.

Measure of ∠D :

Substituting in ∠D = (x - 10)°, we get,

Thus, the measure of angle D is 34°.

Hence, the measure of the angles are ∠A = 91°, ∠C = 89° and ∠D = 34°

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