In a cyclic quadrilateral, if one angle is 80 degrees, what is the maximum possi

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Question: In a cyclic quadrilateral, if one angle is 80 degrees, what is the maximum possible measure of the opposite angle?

Options:

Correct Answer: 100 degrees

Solution:

In a cyclic quadrilateral, opposite angles are supplementary. Therefore, if one angle is 80 degrees, the opposite angle can be 100 degrees.

In a cyclic quadrilateral, if one angle is 80 degrees, what is the maximum possible measure of the opposite angle?

In a cyclic quadrilateral, if one angle is 80 degrees, what is the maximum possible measure of the opposite angle?

Step 1: Understand what a cyclic quadrilateral is. A cyclic quadrilateral is a four-sided figure where all vertices lie on a circle.
Step 2: Know that in a cyclic quadrilateral, opposite angles add up to 180 degrees. This means that if you have one angle, you can find the opposite angle by subtracting it from 180 degrees.
Step 3: Identify the given angle. In this case, one angle is 80 degrees.
Step 4: Calculate the opposite angle by subtracting the given angle from 180 degrees: 180 degrees - 80 degrees = 100 degrees.
Step 5: Conclude that the maximum possible measure of the opposite angle is 100 degrees.

Cyclic Quadrilateral Properties – In a cyclic quadrilateral, the sum of opposite angles is 180 degrees.
Supplementary Angles – Two angles are supplementary if their measures add up to 180 degrees.