A geometry problem by Ossama Ismail

Geometry Level 2

Point $E$ is chosen inside the triangle $ABC$ in such a way that $\angle BED = \angle EBD = 30^\circ$ and $CD = BD$ . Find the measure of $\angle HEG$ in degrees.

The answer is 90.

1 solution

Marta Reece
Apr 12, 2017

$\angle DBE=\angle DEB=>ED=DB=CD, \angle CDE=180^\circ-(180^\circ-30^\circ-30^\circ)=60^\circ=>\triangle CDE$ is equilateral $=>\angle CED=60^\circ$ .

$\angle HEG=\angle CEB=\angle CED+\angle DEB=60^\circ+30^\circ=90^\circ$

A geometry problem by Ossama Ismail

The answer is 90.

1 solution

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