Question

??? quadrilateral abcd ??? is inscribed in this circle. what is the measure of angle c? enter your answer in the box. ?? a quadrilateral inscribed in a circle. the vertices of the quadrilateral lie on the edge of the circle and are labeled as a, b, c,

d. the interior angle a is labeled as left parenthesis 2 x plus 3 right parenthesis degrees. the angle b is labeled as left parenthesis 2 x minus 4 right parenthesis degrees. the angle d is labeled as left parenthesis 3 x plus 9 right parenthesis degrees.

Answer 1

Answer: The measure of angle C is 107 degrees.

When, you have a quadrilateral inscribed in a circle, measure of the opposites sides are supplementary (they add to 180). Therefore, we can write and solve the following equation with angles D and B to find the value of x in the problem.

3x + 9 + 2x - 4 = 180
5x + 5 = 180
5x = 175
x = 35

Now, input x = 35 into the expression for A to find that the measure of angle A is 73.

Since A and C are supplementary:
A + C = 180
73 + C = 180
C = 107

Answer 2

∠C = 107°

Explanation:

Quadrilateral ABCD is inscribed in a circle, and a quadrilateral inscribed in a circle is known as cyclic quadrilateral.

So, ABCD is cyclic quadrilateral.

∠A = 2x + 3

∠B = 2x - 4

∠D = 3x + 9

Also. the sum of opposite angles of the cyclic quadrilateral is supplementary.

⇒ ∠B + ∠D = 180

⇒ 2x - 4 + 3x + 9 = 180

⇒ 5x = 175

⇒ x = 35

Now, ∠A = 73

Also, ∠A + ∠C = 180

⇒ ∠C = 180 - 73

⇒ ∠C = 107°