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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.   \(110^{\circ}\)

Show Worked Solution

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

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

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

Properties of Geometrical Figures, SM-Bank 030

 \(ABCDE\) is a pentagon.
 

  1. Using point \(A\) as one vertex, divide the pentagon into the maximum number of triangles possible.   (1 mark)

  2. Using the angle sum of one triangle, show that the sum of the internal angles of the pentagon is 540°.   (2 marks)

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i.    
         

ii.    \(ABCDE\ \text{can be divided into 3 triangles.}\)

\(\text{Angle sum of a triangle = 180°}\)

\(\text{Angle sum of}\ ABCDE = 3 \times 180^{\circ} = 540^{\circ}\)

Show Worked Solution

i.    
         

ii.    \(ABCDE\ \text{can be divided into 3 triangles.}\)

\(\text{Angle sum of a triangle = 180°}\)

\(\text{Angle sum of}\ ABCDE = 3 \times 180^{\circ} = 540^{\circ}\)