Question

2. Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work.

Answer 1

A cyclic quadrilateral is a quadrilateral whose vertices all touch the circumference of a circle.

Opposite angles in a cyclic quadrilateral add to 180 degrees. Quadrilateral ABCD is a cyclic quadrilateral.

< A+<C=180

Substituting <A and <B values given in figure:

x+2+x-2=180

Adding like terms:

2x=180

Dividing both sides by 2

x=90°

<A=x+2=90+2=92°

<C=x-2=90-2=88°

<D=x-10=90-10=80°

<B+<D=180

<B=180-80=100°

The angles of the quadrilateral ABCD are

<A=92°

<B=100°

<C=88°

<D=80°