The measure of angle A is 135°
Explanation:
Given that the quadrilateral ABCD is inscribed in a circle.
The vertices A, B, C, D lie on the edge of the circle.
The measure of angle A is [tex]\angle A=(3x+6)^{\circ}[/tex]
The measure of angle C is [tex]\angle C=(x+2)^{\circ}[/tex]
We need to determine the measure of angle A
Since, the angles A and C are opposite angles and we know that the opposite angles are supplementary.
Thus, we have,
[tex]\angle A+\angle C=180^{\circ}[/tex]
Substituting the values, we get,
[tex]3x+6+x+2=180[/tex]
[tex]4x+8=180[/tex]
[tex]4x=172[/tex]
[tex]x=43[/tex]
Thus, the value of x is 43
The measure of angle A can be determined by substituting the value of x, we get,
[tex]\angle A=(3x+6)^{\circ}[/tex]
[tex]\angle A=(3(43)+6)^{\circ}[/tex]
[tex]\angle A=(129+6)^{\circ}[/tex]
[tex]\angle A=135^{\circ}[/tex]
Thus, the measure of angle A is [tex]\angle A=135^{\circ}[/tex]
Answer: 77
Step-by-step explanation:
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