Question 14 Marks

In the figure given below, $A D$ is a straight line. $P S$ and $Q R$ are perpendicular to $A D$.
$G H$ is parallel to $I$ and $K L$ is parallel to $M N$.

Q.1. What type of angles are $\angle r$ and $\angle t$ ?
(a) Adjacent angles $\qquad$ (b) Vertically opposite angles
(c) Corresponding angles $\qquad$ (d) Alternate exterior angles
Q.2. The measure of $\angle s =120^{\circ}$. What is the measure of $\angle t ?$
(a) $30^{\circ}$ $\qquad$ (b) $60^{\circ}$ $\qquad$ (c) $90^{\circ}$ $\qquad$ (d) $120^{\circ}$
Q.3. What is the measure of $\angle x$ ?
(a) $45^{\circ}$ $\qquad$ (b) $60^{\circ}$ $\qquad$ (c) $90^{\circ}$ $\qquad$ (d) $120^{\circ}$
Q.4. Which of the following is true for DE and DF?
(a) They are parallel $\qquad$ (b) They intersect at $A$
(c) They intersect at $D$ $\qquad$ (d) They have $A D$ as transversal.

Answer

1. (c) Since, $G H$ is parallel to $I J$ and $G I$ is the transversal.
$
\therefore \angle r=\angle t \quad \text { [corresponding angles] }
$
Hence, $\angle r$ and $\angle t$ are corresponding angles.
2. (b) Given, $G H \| I J$ and $G I$ is the transversal and $\angle s=120^{\circ}$.
We know that if a transversal intersects two parallel lines, then the interior angles on same side of the transversal is supplementary.
$
\begin{array}{lrl}
\therefore \angle s+\angle t=180^{\circ} \\
\Rightarrow 120^{\circ}+\angle t=80^{\circ} \\
\Rightarrow \angle t=180^{\circ}-120^{\circ} \\
\Rightarrow \angle t=60^{\circ}
\end{array}
$
3. (c) Given, $A D$ is a straight line, $P S$ and $Q R$ are perpendicular to $A D$.
When two straight lines intersect each other at $90^{\circ}$ or are perpendicular to each other at the intersection, they form the right angle.
Thus, line $P S$ is perpendicular to $A D, \angle x$ is a right angle i.e. $90^{\circ}$.
Hence, required measure of $\angle x$ is $90^{\circ}$.
4. (c) The lines $D E$ and $D F$ are meet together, thus these are not parallel lines.
Hence, the lines $D E$ and $D F$ intersects at $D$.

View full question & answer→