Mathematics

$$AB\parallel CD$$ and $$ ACM$$ is a straight line $$\angle BAC$$ is equal to:


Answer & Solution

$${108}^{o}$$


SOLUTION
As $$ AB \parallel CD $$ and $$ ACM $$ is a straight line cutting them,  it is called the transversal.

When a transversal cuts two parallel lines, the corresponding angles are equal.
This means $$ \angle BAC = 3{x}^{o} $$

Since $$ LAC $$ is a straight line, we have, $$ \angle LAB + \angle BAC = {180}^{o} $$
$$ => 2{x}^{o} + 3{x}^{o} ={180}^{o}  $$
$$ => 5{x}^{o} = {180}^{o} $$
$$ => {x}^{o} = {36}^{o} $$

$$ => \angle BAC = 3{x}^{o} = 3\times {36}^{o} = {108}^{o} $$

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Single Correct Medium Published on 09th 09, 2020
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