Mathematics

# In the figure, $PQR$ is a straight line. Find $x$. Then complete the following :(i) $\angle AQB=$(ii) $\angle BQP=$(iii) $\angle AQR=$

##### SOLUTION
In the given fig., $\angle{PQA}, \angle{AQB}$ and $\angle{BQR}$ forms a linear pair.

Therefore,

$\angle{PQA} + \angle{AQB} + \angle{BQR} = 180°$

$\left( x + 20° \right) + \left( 2x + 10° \right) + \left( x - 10° \right) = 180°$

$4x + 20° = 180°$

$\Rightarrow x = \cfrac{180° - 20°}{4} = 40°$

Therefore,

$\angle{AQB} = 2x + 10° = 2 \times 40° + 10° = 90°$

$\angle{BQP} = \left( x + 20° \right) + \left( 2x + 10° \right) = 3x + 30° = 3 \times 40° + 30° = 150°$

$\angle{AQR} = \left( 2x + 10° \right) + \left( x - 10° \right) = 3x = 3 \times 40° = 120°$

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Subjective Medium Published on 09th 09, 2020
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