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Question
PQRSTU is a regular hexagon. Determine each angle of ΔPQT.
Solution
\[\text{ A regular hexagon is made up of 6 equilateral triangles } . \]
\[So, ∠PQT = 60° \text{ and } ∠QTP = 30° \]
\[\text{ Since the sum of the angles of ∆ PQT is } 180° , \text{ we have } : \]
\[ ∠P + ∠Q + ∠T = 180\]
\[ \Rightarrow ∠P + 60° + 30°= 180° \]
\[ \Rightarrow ∠P = 180° - 90° \]
\[ \Rightarrow ∠QPT = 90° \]
\[ \therefore \text{ The angles of the triangle are 90° , 60° and } 30° .\]
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