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# In triangle ABC, M and N are the midpoints of BC and AC, respectively. The perpendicular bisectors of BC and AC intersect at a point

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In triangle ABC, M and N are the midpoints of BC and AC, respectively. The perpendicular bisectors of BC and AC intersect at a point O inside the triangle. If angle C = 47 degrees, then find the measure of angle MON, in degrees.

bbelt711  Jul 26, 2017
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In triangle ABC, M and N are the midpoints of BC and AC, respectively. The perpendicular bisectors of BC and AC intersect at a point O inside the triangle. If angle C = $$\gamma$$ = 47 degrees, then find the measure of angle MON = $$\omega$$, in degrees.

Hello bbelt711

The angular sum in each quadrangle is 360 °.
The angular sum in the square ONCM is 360 °.

Then is

$$\omega= 360°-2\times 90°-\gamma\\ \omega= 360°-2\times 90°-47°\\ \\ {\color{blue} \omega =133°}$$

!

asinus  Jul 26, 2017
edited by asinus  Jul 26, 2017

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