Use the information given in the following figure to find :
$x$ (in degrees).

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Solution

We know, by angle sum property, the sum of interior angles of a quadrilateral $= 360^{o}$ .
Given the angles are:
$(3 x - 5^{o}), (8 x - 15^{o}), 2 x + 4^{o} and 90^{o} . 3 x - 5^{o} + 8 x - 15^{o} + 2 x + 4^{o} + 90^{o} = 360^{o} \Rightarrow 13 x - 16^{o} + 90^{o} = 360^{o} \Rightarrow 13 x + 74^{o} = 360^{o} \Rightarrow 13 x = 360^{o} - 74^{o} = 286^{o} \Rightarrow x = \frac{286^{o}}{13} = 22^{o} . ∴ x = 22^{o} .$

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