Question

Classify the given angles as pairs of complementary, linear pair, vertically opposite and adjacent angles.

Accepted Answer

We know that two angles are said to be a pair of complementary angles if their sum is $90 °$ .

Here, we observe that the measures of angles $a$ and $b$ are not given in the question.

So, we cannot calculate and check whether the sum of angles $a$ and $b$ is $90 °$ or not.

Hence, the pair of angles $a$ and $b$ may or may not be complementary.

Again, we know that a linear pair of angles is a pair of adjacent angles made upon the same straight line and must have one common vertex. Since the two adjacent angles are made on the same straight line, the sum of the linear pair of angles always becomes $180 °$ .

Here, the angles $a = ∠ A O B$ and $b = ∠ B O C$ are not made on the same straight line although they have the same vertex $O$ .

So, the angles $a$ and $b$ do not form a linear pair of angles.

Now, we know that vertically opposite angles are a pair of angles that are formed when two lines intersect each other.

Here, we observe that all the lines $\vec{O A}, \vec{O B}$ and $\vec{O C}$ are originating from the same point $O$ . So, they are not intersecting lines.

Hence, the given angles $a$ and $b$ are not a pair of vertically opposite angles.

Lastly, we know that the adjacent angles are two angles that have a common vertex and a common side, such that the angles do not overlap.

Here, we observe that angles $a$ and $b$ have a common vertex $O$ and a common side $\vec{O B}$ . The sides $\vec{O A}$ of $a$ and $\vec{O C}$ of $b$ are at the two other sides of the common side $\vec{O B}$ , and so, angles $a$ and $b$ do not overlap.

Clearly, angles $a$ and $b$ satisfy the above definition of the adjacent angles.

Hence, angles $a$ and $b$ are a pair of adjacent angles.

Classify the given angles as pairs of complementary, linear pair, vertically opposite and adjacent angles.

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