Question

Consider the following statements:

Statement I: All complementary angles are adjacent angles.

Statement II: When the sum of two adjacent angle measures is ${180}^o,$ they form a straight line.

• A. Both the statements are correct.
• B. Only statement I is correct.
• C. Only statement II is correct.
• D. None of the above.

Answer 1

The correct option is C Only statement II is correct.

Adjacent angles are the angles that share a common ray.
For example,

here the $\angle {20}^o$ and $\angle {60}^o$ are adjacent to each other.
They share a common ray, shown here by the dashed line.

Consider the following figure:
Here, $\angle AEB$ and $\angle CBD$ are complementary angles. However, they are not adjacent angles.
$\therefore$ Statement I is wrong.


The sum of these angles is $\angle {120}^o+\angle {60}^o=\angle {180}^o.$
Also, they form a straight line as they are placed adjacent to each other.
$\therefore$ Statement II is correct,