Quadrilateral abcd is inscribed in a circle. what is the measure of angle c? show your work.

92

Step-by-step explanation:

Remark

This kind of quadrilateral (one inscribed in a circle) is called a cyclic quadrilateral.

It has the unusual properties of opposite angles being supplementary. That means they add to 180o

Givens

B + D = 180 degrees

C + A = 180 degrees

Solution

Work with <B + <D = 180o

x + 24 + x + 10 = 180                  Collect like terms on the left.

2x + 34 = 180                              Subtract 34 for both sides

2x +34-34 = 180-34                    Combine

2x = 146                                      Divide by 2

x = 146/2                

x = 73

Now work with A  + C = 180

A = x + 15

A = 73 + 15

A = 88

88 + C = 180                             Subtract 88 from both sides.

88 - 88 + C = 180 - 88

C = 92

26

step-by-step explanation: