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Properties of Geometric Figures, SM-Bank 040

 

Determine the value of the two unknown angles in the quadrilateral above, giving reasons for your answer.     (3 marks)

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\(\text{Angle sum of quadrilaterals = 360°:} \)

\(360\) \(=5x+3x+79+105 \)  
\(8x\) \(=360-184\)  
\(x^{\circ}\) \(=\dfrac{176}{8}\)  
  \(=22^{\circ}\)  

 
\(\text{Unknown angle 1}\ = 3 \times 22 = 66^{\circ}\)

\(\text{Unknown angle 2}\ = 5 \times 22 = 110^{\circ}\)

Show Worked Solution

\(\text{Angle sum of quadrilaterals = 360°:} \)

\(360\) \(=5x+3x+79+105 \)  
\(8x\) \(=360-184\)  
\(x^{\circ}\) \(=\dfrac{176}{8}\)  
  \(=22^{\circ}\)  

 
\(\text{Unknown angle 1}\ = 3 \times 22 = 66^{\circ}\)

\(\text{Unknown angle 2}\ = 5 \times 22 = 110^{\circ}\)