MathDB

2

Part of 2022 Greece Junior Math Olympiad

Problems(1)

Let's play with angles

Source: Greece Junior National Olympiad 2022, Problem 2

2/26/2022
Let ABCABC be an isosceles triangle, and point DD in its interior such that DB^C=30∘,DB^A=50∘,DC^B=55∘D \hat{B} C=30^\circ, D \hat{B}A=50^\circ, D \hat{C}B=55^\circ
(a) Prove that B^=C^=80∘\hat B=\hat C=80^\circ. (b) Find the measure of the angle DA^CD \hat{A} C.
geometry