Beautiful Geometry 1

Angles Inside a Quadrilateral

What’s the angle?

SOLUTION

Let the quadrilateral be $ABCD$ . Using the provided angles, we can find that $∠BCA=90°$ and therefore point $C$ belongs to the circle with diameter $AB$ . Also, we can see that $△AOD$ is isosceles, $OA=OD=OB$ , and point $D$ also lies on the circle with diameter $AB$ .

Using the provided angles, we can find that $∠BCA=90°$ and therefore point $C$ belongs to the circle with diameter $AB$ . Also, we can see that $△AOD$ is isosceles, $OA=OD=OB$ , and point $D$ also lies on the circle with diameter $AB$ .

Therefore, $ABCD$ is inscribed in a circle with center $O$ , and $∠ACD=∠AOD/2=40°$ .

Angles Inside a Quadrilateral

Puzzle Newsletter