Question

Find the measure of $\angle 1$.

• A. 82${}^{\circ }$
• B. 42${}^{\circ }$
• C. 62${}^{\circ }$
• D. 112${}^{\circ }$

Answer 1

The correct option is B 42${}^{\circ }$

In the given figure, m II n and t is the transversal.
Here, 8x - 4 = 6x + 8 {Corresponding anglesl}
$\Rightarrow$ 8x - 6x = 8 + 4
$\Rightarrow$ 2x = 12
$\Rightarrow$ x = 6
$\Rightarrow$ 6x + 8 = 6 $\times$ 6 + 8 = 36 + 8 = 42${}^{\circ }$
Now, $\angle 1$ = 6x + 8 {Vertically opposite angles}
$\Rightarrow$ $\angle 1$ = 42${}^{\circ }$
$\therefore \angle 1$ is 42${}^{\circ }$.