Question

Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral.
Can someone please explain to me how you do this?

Answer 1

Here is a reference to the Inscribed Quadrilateral Conjecture it says that opposite angles of an inscribed quadrilateral are supplemental.

Explanation:

The conjecture, #angleA and angleC# allows us to write the following equation:

#angleA + angleC=180^@#

Substitute the equivalent expressions in terms of x:

#x+2+ x-2 = 180^@#

#2x = 180^@#

#x = 90^@#

From this we can compute the measures of all of the angles.

#angleA=92^@#

#angleB=100^@#

#angleC=88^@#

#angleD= 80^@#

Answer 2

Answer:  m< A = 92

               m<B = 100

               m<C = 88

               m< D 80

Step-by-step explanation:

(x+2) + (x-2) = 180

2x = 180  

x=90

A= x+2=90+2=92

C= x-2=90-2=88

D=x-10=90-10=80

B=360-(92+88+80)=360-260=100