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UKMT Junior Mathematical Olympiad, 2019

Algebra Difficulty 2.0 Junior Prove it United Kingdom

The diagram shows three figures. The first is a triangle with an angle of $a°$ at the apex and angles of $2a°$ and $2a°$ at the base. The second is a square with one side labelled $\left(\frac{a}{4}\right)^2$ cm and an adjacent side labelled $b^4$ cm. The third is a right-angled triangle with the right angle at one vertex, an angle of $b(b+1)(b+2)°$ at another vertex, and an angle of $c°$ at the third vertex. What is the value of $c$ ?

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