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

Mathematics

1 answer:

Nadusha1986 [10]3 years ago

4 0

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^@#

<span>#angleD= 80^@#</span>

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