Question

Find the value of the unknown x in the following diagrams:

Answer 1

The sum of all interior angles of a triangle is \(180°\). By using this property, these problems can be solved as follows.

(i) \(x + 50° + 60°\) 
= \(180° x + 110° = 180° x\) 
= \(180° -110° = 70°\)

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(ii) \(x + 90° +30°\) 
= \(180° x + 120°\) =\(180° x\) 
= \(180° - 120°\) 
=\(60°\)

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(iii) \(x + 30° + 110° =180° x + 140° = 180°\)
\(x = 180° - 140° = 40°\)

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(iv) \(50° + x + x = 180°\)
\(50° + 2x = 180°\)
\(2x = 180° - 50° = 130°\)
\(x= \frac{130\degree}{2}=65\degree\)

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(v) \(x + x + x = 180°\)
\(3x = 180°\)
\(x=\frac{180}{3}=60\degree\)

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(vi) \(x + 2x + 90° = 180°\)
\(3x = 180° - 90° = 90 º\)
\(x = \frac{90\degree}{3}=30\degree\)