Question

If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio $3:7$, then the measure of the larger angle is

• A. ${54}^{\circ }$
• B. ${120}^{\circ }$
• C. ${126}^{\circ }$
• D. ${108}^{\circ }$

Answer 1

Answer: (C)

${126}^{\circ }$

Let the angles be $3x$ and $7x$.

We know that sum of two interior angles on the same side of transversal is ${180}^{\circ }$.

$3x+7x={180}^{\circ }$

$\Rightarrow 10x={180}^{\circ }$

$\Rightarrow x={18}^{\circ }$

Therefore, the greater angle is $7x=7\times 18={126}^{\circ }$