Question 14 Marks

Saumya sketched four straight lines all intersecting at a point $O$. She studied the angles formed due to the intersection of these lines and found that $\angle B O C=90^{\circ}$.

Q.1. Which of the following is a pair of perpendicular lines?
(a) AB, GH$\quad$ (b) CD, АВ$\quad$(c) EF, GH$\quad$(d) CD, EF
Q.2. Which of the following is a pair of complementary angles?
(a) $\angle E O C, \angle C O B$$\quad$(b) $\angle G O F, \angle F O H$$\quad$(c) $\angle A O H, \angle H O D$$\quad$(d) $\angle B O F, \angle F O A$
Q.3. Which of the following is a pair of supplementary angles?
(a) $\angle C O E, \angle E O H$$\quad$(b) $\angle B O F, \angle F O A$$\quad$(c) $\angle G O F, \angle F O D$$\quad$(d) $\angle E O G, \angle G O B$
Q.4. Which of the following is a pair of vertically angles?
(a) $\angle E O A, \angle F O B$$\quad$(b) $\angle C O G, \angle D O F$$\quad$(c) $\angle F O H, \angle G O C$$\quad$(d) $\angle A O G, \angle H O F$

Answer

1. (b): $\angle B O C=90^{\circ} \Rightarrow C D$ and $A B$ are perpendicular lines.
2. (c): $\angle A O D=\angle B O C=90^{\circ}$. [vertically opposite angles]
$
\therefore \angle A O H+\angle H O D=\angle A O D=90^{\circ} .
$
So, $\angle A O H$ and $\angle H O D$ form a pair of complementary angles.
3. (b): $A B$ is a straight line.
$\therefore \angle B O F$ and $\angle F O A$ form a linear pair, i.e., $\angle B O F+\angle F O A=180^{\circ}$.
So, $\angle B O F$ and $\angle F O A$ are supplementary angles.
4. (a): $\angle E O A$ and $\angle F O B$ form a pair of vertically opposite angles because $A B$ and $E F$ are straight lines intersecting at point $O$.

View full question & answer→