Triangle inscribed in a circle

Geometry Level 2

In the diagram above, triangle $ABE$ is inscribed in the circle, and line segment $\overline {DC}$ is tangent to the circle at point $E$ with $\angle AEC = 150^\circ$ .

Find the measure of $\angle ABE$ in degrees.

The answer is 30.

1 solution

Viki Zeta
Mar 10, 2017

$\angle AEC + \angle AED = 180 \\ \implies \angle AED = 180 - 150 = 30 \\ \text{using alternate segment theorem, } \\ \angle AED = \angle ABE = 30$

Triangle inscribed in a circle

The answer is 30.

1 solution

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