Given:
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
Value of z:
We know the property that the opposite angles of a quadrilateral inscribed in a circle are supplementary.
Thus, we have;
[tex]\angle A+ \angle C=180^{\circ}[/tex]
Substituting the values, we have;
[tex]14z-7+8z=180[/tex]
[tex]22z-7=180[/tex]
[tex]22z=187[/tex]
[tex]z=8.5[/tex]
Thus, the value of z is 8.5
Measure of ∠A:
The measure of ∠A can be determined by substituting the value of z.
Thus, we have;
[tex]\angle A=14(8.5)-7[/tex]
[tex]\angle A=119-7[/tex]
[tex]\angle A=112^{\circ}[/tex]
Thus, the measure of ∠A is 112°
Measure of ∠C:
The measure of ∠C can be determined by substituting the value of z.
Thus, we have;
[tex]\angle C=8(8.5)[/tex]
[tex]\angle C =68^{\circ}[/tex]
Thus, the measure of ∠C is 68°
Measure of ∠D:
The measure of ∠D can be determined by substituting the value of z.
Thus, we have;
[tex]\angle D=10(8.5)[/tex]
[tex]\angle D=85^{\circ}[/tex]
Thus, the measure of ∠D is 85°
Measure of ∠B:
The angles B and D are supplementary.
Thus, we have;
[tex]\angle B+ \angle D=180^{\circ}[/tex]
Substituting the values, we get;
[tex]\angle B+ 85^{\circ}=180^{\circ}[/tex]
[tex]\angle B=95^{\circ}[/tex]
Thus, the measure of ∠B is 95°
