Question

Given that lines m and n are parallel, find the measure of $\angle 1$.

• A. 144°
• B. 121°
• C. 153°
• D. 105°

Answer 1

The correct option is A 144°

We know that if a transversal intersects two parallel lines, then the alternate exterior angles will be equal.
$\Rightarrow x^2=x+{30}^{\circ }$
$\Rightarrow x^2-x-{30}^{\circ }=0$
$\Rightarrow x^2-6x+5x-{30}^{\circ }=0$
(By splitting the middle term of quadratic equation)
Taking the common factors out, we get
$x(x-6^{\circ })+5(x-6^{\circ })=0$
$\Rightarrow (x-6^{\circ })(x+5^{\circ })=0$
$\Rightarrow x=6^{\circ }$ or $x=-5^{\circ }$

Since the measure of an angle cannot be negative, consider the positive root $x=6^{\circ }$

We know that angles on a straight line sum up to ${180}^{\circ }$.

$\Rightarrow x^2+\angle 1={180}^{\circ }$ (Linear pair)
$\Rightarrow (6^2{)}^{\circ }+\angle 1={180}^{\circ }$
$\Rightarrow {36}^{\circ }+\angle 1={180}^{\circ }$
$\Rightarrow \angle 1={180}^{\circ }-{36}^{\circ }$
$\Rightarrow \angle 1={144}^{\circ }$