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

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54^{\circ}

120^{\circ}

126^{\circ}

108^{\circ}

answer is C.

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Detailed Solution

We have been given,
Two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio

3 : 7

.
Assuming the angles are

3 x

and

7 x

.
We are aware, the sum of two interior angles on the same transverse side is 180°.
Therefore, we can say,

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

(Interior angles)
Solving the equation,

\Rightarrow 10 x = 180^{\circ}

\Rightarrow x = 18^{\circ}

Calculating the greater angle,
Substituting the values,

\Rightarrow 7 x

\Rightarrow 7 \times 18

\Rightarrow 126^{\circ}

Therefore, the larger angle is 126o.
Hence, option 3 is correct.

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