Question

PQRSTU is a regular hexagon. Determine each angle of ΔPQT.

 

Answer 1

\[\text{ A regular hexagon is made up of 6 equilateral triangles }  . \]

\[So, ∠PQT = 60° \text{ and } ∠QTP = 30° \]

\[\text{ Since the sum of the angles of ∆ PQT is } 180° , \text{ we have } : \]

\[ ∠P + ∠Q + ∠T = 180\]

\[ \Rightarrow ∠P + 60° + 30°= 180° \]

\[ \Rightarrow ∠P = 180° - 90° \]

\[ \Rightarrow ∠QPT = 90° \]

\[ \therefore \text{ The angles of the triangle are 90° , 60°  and }  30° .\]