List all the linear pairs and vertically opposite angles you observe in Fig. 5.3:

Question

Homi · Accepted Answer

When two lines cross each other, they form different types of angles.

Step 1 — Identifying Linear Pairs

Linear pairs are two angles that are next to each other. They form a straight line together. The sum of their measures is always 180 degrees.

Let us look at the diagram. Line $l$ and line $m$ intersect. We can find pairs of angles that form a straight line.

Angles $\angle a$ and $\angle b$ are next to each other on line $m$ . They form a straight line.
Angles $\angle b$ and $\angle c$ are next to each other on line $l$ . They form a straight line.
Angles $\angle c$ and $\angle d$ are next to each other on line $m$ . They form a straight line.
Angles $\angle d$ and $\angle a$ are next to each other on line $l$ . They form a straight line.

Diagram 1

Step 2 — Identifying Vertically Opposite Angles

Vertically opposite angles are formed when two lines cross. They are directly opposite each other. These angles are always equal in measure.

Let us look at the diagram again. Line $l$ and line $m$ cross each other. We can find angles that are opposite to each other.

Angle $\angle a$ is opposite to angle $\angle c$ .
Angle $\angle b$ is opposite to angle $\angle d$ .

Diagram 2

Answer

Linear Pairs: $\angle a$ and $\angle b$ , $\angle b$ and $\angle c$ , $\angle c$ and $\angle d$ , $\angle d$ and $\angle a$ . Pairs of Vertically Opposite Angles: $\angle b$ and $\angle d$ , $\angle a$ and $\angle c$ .

Question 1

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