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

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18