# The bisectors AD and BE of triangle ABC meet at point O. Find the angle C of the triangle if the angle AOE = 50 degrees.

September 30, 2021 | education

| The AOE angle given by condition is the outer angle for the AOB triangle.

Let’s use the triangle outer angle theorem and write:

∠ AOE = ∠ ABO + ∠ BAO = 1/2 ∠ ABC + 1/2 ∠ BAC = 50 °.

We get that in triangle ABC the sum of two angles is equal to:

∠ ABC + ∠ BAC = 100 °.

We find the degree measure of the angle C of the triangle ABC:

∠ С = 180 ° – (∠ ABC + ∠ BAC) = 180 ° – 100 ° = 80 °.

Answer: the angle C of the triangle ABC is 80 °.

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