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

On this picture is shown a quadrilateral inscribed in a circle and by the Inscribed Quadrilateral Theorem the angles on the opposite vertices are supplementary, or in other words are equals to 180 degrees. 

On this exercise it is asked to find the measure of angle B, First of all, you need to find the value of x. To so you have to select two opposite angles on this case angles A and C.

m<A+m<C=180      Substitute the given values for angles A and C
    x+2+x-2=180       Combine like terms
             2x=180       Divide by 2 in both sides to isolate x
               x=90

Now, that the value of x is known you can substitute it in the expression representing angle D, and then subtract that number from 180 to find the measure of angle B.

m<D=x-10             Substitute the value of x
m<D=90-10           Combine like terms
m<D=80

m<B=180-m<D       Substitute the value of angle D
m<B=180-80           Combine like terms 
m<B=100

The measure of angle B is 100 degrees, and the value of x is 90.