Question

A quadrilateral is inscribed in circle O. The angle measures of the quadrilateral, in degrees, are given by the expressions shown in the figure. B What is the measure of angle C? A. B. 15° D. 165° C. 75° 65° 130 - x 7x - 20 0 4x + 35 95-2x​

Answer 1

Answer:Therefore, the measure of angle C is 75 degrees.

Step-To find the measure of angle C in the given quadrilateral, we need to use the fact that the angles of a quadrilateral add up to 360 degrees.

Let's denote the angle measures as follows:

Angle A = 130 - x

Angle B = 7x - 20

Angle C = 4x + 35

Angle D = 95 - 2x

Using the fact that the sum of the angles in a quadrilateral is 360 degrees, we can set up the equation:

(130 - x) + (7x - 20) + (4x + 35) + (95 - 2x) = 360

Simplifying the equation:

130 + 7x - x - 20 + 4x + 35 + 95 - 2x = 360

12x + 240 = 360

12x = 360 - 240

12x = 120

x = 120/12

x = 10

Now that we have the value of x, we can substitute it back into the expression for angle C:

Angle C = 4x + 35

Angle C = 4(10) + 35

Angle C = 40 + 35

Angle C = 75

Therefore, the measure of angle C is 75 degrees.