Question

In the following figure, line $M$ and line $N$ are parallel. Which of the answer choices does NOT necessarily add up to ${180}^{\circ }$?

• A. $\angle a+\angle b+\angle f$
• B. $\angle a+\angle d$
• C. $\angle e+\angle g$
• D. $\angle b+\angle e+\angle f$
• E. None.

Answer 1

Answer: (C)

In the given figure, $\angle e+\angle g$ does not add up to $\mathring{180}$, as they are alternate angles and are equal, $\angle e=\angle g$
where as:
A. $\angle a$ will be equal to sum of $\angle e$ and $\angle f$ as a is exterior angle and angle $e$ and angle $f$ are opposite interior angles.
So, $\angle a+\angle b+\angle f=\mathring{180}$
B. $\angle a+\angle d=\mathring{180}$ $=$ interior angles on the same side of transversal is always supplementary
C. $\angle a+\angle e+\angle f=\mathring{180}$ $=3$ angles of a triangle always measure $180$ degree.
D. $\angle d+\angle e=\mathring{180}$ $=$ adjacent angles creating a straight line are supplementary.