In Fig. 5.2, if is , can you figure out the measurements of , and , without drawing and measuring them?

Question

Homi · Accepted Answer

We will use the properties of angles formed when two lines intersect, specifically linear pairs and vertically opposite angles.

Step 1 — Find angle b

Angles $a$ and $b$ are next to each other on a straight line. They form what we call a linear pair. Angles in a linear pair always add up to $\mathbf{180^\circ}$ . We know that angle $a$ is $\mathbf{120^\circ}$ . So, to find angle $b$ , we subtract angle $a$ from $\mathbf{180^\circ}$ .

$\angle b = 180^\circ - \angle a$

$= 180^\circ - 120^\circ$

$\boxed{\angle b = 60^\circ}$

Diagram 1

Step 2 — Find angle c

Angles $a$ and $c$ are opposite to each other. They are formed by the intersection of the two lines. These are called vertically opposite angles. Vertically opposite angles are always equal in measure. Since angle $a$ is $\mathbf{120^\circ}$ , angle $c$ must also be $\mathbf{120^\circ}$ .

$\angle c = \angle a$

$\boxed{\angle c = 120^\circ}$

Step 3 — Find angle d

Angles $b$ and $d$ are also opposite to each other. They are vertically opposite angles. Vertically opposite angles are always equal. We found that angle $b$ is $\mathbf{60^\circ}$ . So, angle $d$ must also be $\mathbf{60^\circ}$ .

$\angle d = \angle b$

$\boxed{\angle d = 60^\circ}$

Answer

(i) $\angle b = 60^\circ$ (ii) $\angle c = 120^\circ$ (iii) $\angle d = 60^\circ$

Question 3

Answer

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