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MathNet 2022-part-02 — 197 problems (EN–VI) Question 134

Math Olympiad Vault · MathNet 2022-part-02 — 197 problems (EN–VI)

Question 134

Let $AB\Gamma$ be an isosceles triangle and a point $\Delta$ in its interior such that $\Delta\hat{B}\Gamma = 30^\circ$, $\Delta\hat{B}A = 50^\circ$, $B\hat{\Gamma}\Delta = 55^\circ$.

a. Prove that $\hat{B} = \hat{\Gamma} = 80^\circ$

b. Find the measure of the angle $\Delta\hat{A}\Gamma$.