Quadrilateral ABCD is inscribed in a circle.

What is the measure of angle A?

Enter your answer in the box.

m∠A=
°

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 3 x plus 6 right parenthesis degrees. The angle C is labeled as left parenthesis x plus 2 right parenthesis degrees.

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

The measure of angle C is

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,

Substituting the values, we get,

Thus, the value of x is 43

The measure of angle A can be determined by substituting the value of x, we get,

Thus, the measure of angle A is

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)