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Properties of Geometric Figures, SM-Bank 041

A pentagon is pictured below.
 

  1. By drawing triangles from one vertex, or otherwise, calculate the sum of the internal angles of a pentagon.   (1 mark)

  2. Determine the value of \(x^{\circ}\) in the pentagon.     (2 marks)
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i.    \(540^{\circ}\)

ii.   \(110^{\circ}\)

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i.    \(\text{Pentagon can be divided into 3 triangles (from one chosen vertex).}\)

\(\text{Sum of internal angles}\ = 3 \times 180 = 540^{\circ}\)
 

ii.    \(540\) \(=x + 2 \times 90 + 135+115 \)  
\(540\) \(=x+430\)  
\(x^{\circ}\) \(=540-430\)  
  \(=110^{\circ}\)