Respuesta :
The measure of angle C is 107°
Explanation:
Given that ABCD is a quadrilateral.
The vertices A, B, C, D lie on the edge of the circle.
The measure of angle A is [tex]\angle A=(2x+3)^{\circ[/tex]
The measure of angle B is [tex]\angle B=(2x-4)^{\circ}[/tex]
The measure of angle D is [tex]\angle D=(3x+9)^{\circ}[/tex]
We need to determine the measure of angle C
Since, we know that the opposite angles B and D are supplementary.
Thus, we have,
[tex]\angle B+\angle D=180^{\circ}[/tex]
Substituting the values, we get,
[tex]2x-4+3x+9=180[/tex]
[tex]5x+5=180[/tex]
[tex]5x=175[/tex]
[tex]x=35[/tex]
Thus, the value of x is 35
Substituting the value of x in the measures of angles A, B and D, we get,
[tex]\angle A=(2(35)+3)^{\circ[/tex]
[tex]\angle A=(70+3)^{\circ[/tex]
[tex]\angle A=73^{\circ[/tex]
Similarly, [tex]\angle B=(2x-4)^{\circ}[/tex]
[tex]\angle B=(2(35)-4)^{\circ}[/tex]
[tex]\angle B=(70-4)^{\circ}[/tex]
[tex]\angle B=66^{\circ}[/tex]
For angle D, we have,
[tex]\angle D=(3(35)+9)^{\circ}[/tex]
[tex]\angle D=(105+9)^{\circ}[/tex]
[tex]\angle D=114^{\circ}[/tex]
Now, we shall find the measure of angle C
Since, we know that all the angles in a quadrilateral add up to 360°
Thus, we have,
[tex]\angle A+\angle B+\angle C+\angle D=360^{\circ[/tex]
Substituting the values of A, B and D, we get,
[tex]73^{\circ}+66^{\circ}+\angle C+114^{\circ}=360^{\circ}[/tex]
[tex]253^{\circ}+\angle C=360^{\circ}[/tex]
[tex]\angle C=107^{\circ}[/tex]
Thus, the measure of angle C is 107°
Answer:
measure of angle C is 107°
Step-by-step explanation:
Verified correct with test results.
