Mathematics

# $\angle A$ and $\angle B$ are liner pair of angles. If $4\angle A=5\angle B.$ then find $\angle A$ and $\angle B.$

##### SOLUTION
Since $\angle{A}$ and $\angle{B}$ are linear pair.
Therefore,
$\angle{A} + \angle{B} = 180° ..... \left( 1 \right)$
Also,
$4 \angle{A} = 5 \angle{B} \quad \left( \text{Given} \right)$
$\Rightarrow \angle{A} = \cfrac{5}{4} \angle{B} ..... \left( 2 \right)$
From equation $\left( 1 \right) \& \left( 2 \right)$, we have
$\cfrac{5}{4} \angle{B} + \angle{B} = 180°$
$\Rightarrow \angle{B} = 180° \times \cfrac{4}{9} = 80°$
Substituting the value of $\angle{B}$ in equation $\left( 2 \right)$, we have
$\angle{A} = \cfrac{5}{4} \times 80° = 100°$

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Subjective Medium Published on 09th 09, 2020
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