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<u>Given</u>:
Given that the quadrilateral ABCD is inscribed in the circle.
The measure of ∠A is (14z - 7)°
The measure of ∠C is (8z)°
The measure of ∠D is (10z)°
We need to determine the measures of ∠A, ∠B, ∠C and ∠D
<u>Value of z:</u>
We know the property that the opposite angles of a quadrilateral inscribed in a circle are supplementary.
Thus, we have;
Substituting the values, we have;
Thus, the value of z is 8.5
<u>Measure of ∠A:</u>
The measure of ∠A can be determined by substituting the value of z.
Thus, we have;
Thus, the measure of ∠A is 112°
<u>Measure of ∠C:</u>
The measure of ∠C can be determined by substituting the value of z.
Thus, we have;
Thus, the measure of ∠C is 68°
<u>Measure of ∠D:</u>
The measure of ∠D can be determined by substituting the value of z.
Thus, we have;
Thus, the measure of ∠D is 85°
<u>Measure of ∠B:</u>
The angles B and D are supplementary.
Thus, we have;
Substituting the values, we get;
Thus, the measure of ∠B is 95°