Chase the angle if you can

Geometry Level 1

Triangle $DEC$ is inscribed in a circle with center at $O$ . Line $AB$ is a tangent to the circle at $C$ . $\angle EDC=45^\circ$ and $\angle DCA=50^\circ$ . Find $\angle DOE$ .

175^\circ

160^\circ

145^\circ

170^\circ

1 solution

Christian Daang
Oct 19, 2017

Note that arc( $DC = 2*50^{\circ} = 100^{\circ}$ ) and arc( $CE = 2*45^{\circ} = 90^{\circ}$ )

Hence, $\angle DOE = \text{arc} \ ED = 360^{\circ} - (100^{\circ} + 90^{\circ}) = \boxed{170^{\circ}}$ .

Chase the angle if you can

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