Question

State whether the given information be used to prove that two lines are parallel and also state which lines.

$\text{m}\angle \mathbf{8}+\text{m}\angle \mathbf{9}=\mathbf{180}$

Short answer

The given condition can prove two lines parallel and the lines that are parallel are $\text{c}\parallel \text{d}$.

Step-by-step solution

- Consider the diagram. 

Here, $m\angle 8+m\angle 9=180$.

- Show the calculation.

Using the theorem which states-

If two lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel.

Since, angle $\angle 8$ and $\angle 9$ are same interior angles on same side formed by line $a$, which is the transversal line given their sum is $180°$, then by the theorem,$c\parallel d$.

- State the conclusion.

Therefore, the condition $m\angle 8+m\angle 9=180$ proves $c\parallel d$.