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MathNet 2018-part-01 — 181 problems (EN–VI) Question 176

Math Olympiad Vault · MathNet 2018-part-01 — 181 problems (EN–VI)

Question 176

Triangle $ABC$ below has a point $D$ on its side $AB$ such that $AB = CD$, $\angle ABC = 100^{\circ}$ and $\angle DCB = 40^{\circ}$.
Question illustration

a) What is the measure of the angle $B\hat{D}C$?

b) What is the measure of the angle $A\hat{C}D$?