Question

In the above figure, if AB $\parallel$ CD, then which of the following is true?

• A. $\angle$$APQ$ = $\angle$ $QPB$
• B. $\angle$$APQ$ = $\angle$ $CQP$
• C. $\angle$$APQ$ + $\angle$ $CQP$ = $180$ ${}^{\circ }$
• D. $\angle$$CQP$ + $\angle$ $QPB$ = $180$ ${}^{\circ }$

Answer 1

The correct option is C $\angle$$APQ$ + $\angle$ $CQP$ = $180$ ${}^{\circ }$

From Euclid's 5th postulate, we know that the sum of interior angles on the same side of transversal is equal to 180 ${}^{\circ }$.

$\angle$$APQ$ and $\angle$ $CQP$ are interior angles on the same side of the transversal
$\therefore$ Their sum is equal to 180 ${}^{\circ }$.