In a cyclic quadrilateral, an exterior angle at one corner is (2x + 12)°…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
In a cyclic quadrilateral, an exterior angle at one corner is . The interior opposite angle is . Find and the exterior angle.
Need a reminder? The key ideaShow
An exterior angle of a cyclic quadrilateral is equal to the interior opposite angle. The exterior angle and the interior angle at the same corner lie on a straight line, so they add up to . Angles in the same part of a circle, on the same chord, are equal.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The equation. .
Step 2. Solve. , so .
Step 3. The angle. , and .
Answer: , and the exterior angle is .
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