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AMO 2027 Grades 8-9 SET 18 - Self-study Question 11

AMO · AMO 2027 Grades 8-9 SET 18 - Self-study

Question 11

Exercise 21. Point $M$ is placed inside the square $ABCD$ in such a way that
$$\angle MAD:\angle MBA:\angle MCD=2:4:7.$$
What is measure of $\angle MCA$ in degrees?

**Editorial input convention:** Label the square vertices A,B,C,D in cyclic order, with M strictly inside. Enter the angle measure in degrees.