Question

Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral.

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^@#