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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