Question 7

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

Draw some lines perpendicular to the lines given on the dot paper in Fig. 5.10.

In Fig. 5.11, mark the parallel lines using the notation given above (single arrow, double arrow etc.). Mark the angle between perpendicular lines with a square symbol.

(a) How did you spot the perpendicular lines?

(b) How did you spot the parallel lines?

In the dot paper following, draw different sets of parallel lines. The line segments can be of different lengths but should have dots as endpoints.

Using your sense of how parallel lines look, try to draw lines parallel to the line segments on this dot paper.

(a) Did you find it challenging to draw some of them? (b) Which ones? (c) How did you do it?

In Fig. 5.13, which line is parallel to line $a$ — line $b$ or line $c$? How do you decide this?

Find the angles marked below.

Find the angle represented by $a$.

In the figures below, what angles do $x$ and $y$ stand for?

In Fig. 5.33, $\angle ABC = 45^\circ$ and $\angle IKJ = 78^\circ$. Find angles $\angle GEH$, $\angle HEF$, $\angle FED$

In Fig. 5.34, $AB$ is parallel to $CD$ and $CD$ is parallel to $EF$. Also, $EA$ is perpendicular to $AB$. If $\angle BEF = 55^\circ$, find the values of $x$ and $y$.

What is the measure of angle $\angle \text{NOP}$ in Fig. 5.35?

[Hint: Draw lines parallel to LM and PQ through points N and O.]