Question
If a transversal intersects two parallel lines, and the difference of two interior angles on the same side of a transversal is $20^\circ ,$ find the angles.
✓
Answer
Let the two interior angles on the same side of transversal are $x$ and $y.$
Given, their difference is $20^\circ .$
$\therefore \text{x}-\text{y}=20^\circ$
$\Rightarrow \text{y}=\text{x}-20^\circ$
Since, $l$ amd $m$ are parallel and $p$ is transversal.
Then, $\text{x}+\text{y}=180^\circ [ \because$ sum of an interior angles is $180^\circ ]$
$\therefore\text{x}+\text{x}-20^\circ =180^\circ[ $from Eq,$(i)]$
$\Rightarrow 2\text{x}=180^\circ+20^\circ$
$\Rightarrow 2\text{x}=200^\circ$
$\Rightarrow\text{x}=\frac{200^\circ}{2}=100^\circ$
Now, $\text{y}=\text{x}-20^\circ$
$\therefore\text{y}=100^\circ-20^\circ= 80^\circ$
Therefore, the angles are $100^\circ $ and $80^\circ ,$ respectively
Given, their difference is $20^\circ .$
$\therefore \text{x}-\text{y}=20^\circ$
$\Rightarrow \text{y}=\text{x}-20^\circ$
Since, $l$ amd $m$ are parallel and $p$ is transversal.
Then, $\text{x}+\text{y}=180^\circ [ \because$ sum of an interior angles is $180^\circ ]$
$\therefore\text{x}+\text{x}-20^\circ =180^\circ[ $from Eq,$(i)]$
$\Rightarrow 2\text{x}=180^\circ+20^\circ$
$\Rightarrow 2\text{x}=200^\circ$
$\Rightarrow\text{x}=\frac{200^\circ}{2}=100^\circ$
Now, $\text{y}=\text{x}-20^\circ$
$\therefore\text{y}=100^\circ-20^\circ= 80^\circ$
Therefore, the angles are $100^\circ $ and $80^\circ ,$ respectively
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