If ray $PQ$ and $RS$ are parallel as shown in the figure, then find $a+b+c$.

 

In the given figure $AC\parallel BD$ and $AE\parallel BF$. The measure of $x$ is:

In the given figure, if $\angle BOC=7x+20°$ and $\angle COA=3x+30°$, then the value of $x$ for which $AOB$ becomes a straight line is:

In the section, each question has two matching lists. Choices for the correct combination of elements from List-I and List-II are given as options $\left(a\right), \left(b\right), \left(c\right)$ and $\left(d\right)$ out of which, one is correct.

Match the following:

In the section, each question has two matching lists. Choices for the correct combination of elements from List-I and List-II are given as options $\left(a\right), \left(b\right), \left(c\right)$ and $\left(d\right)$ out of which, one is correct.

Match the following:

Match the value of $x$ given in List-I and List-II with the figure given in List-I.

	List-I		List-II
$\left(P\right)$		$1$	$x=47°$
$\left(Q\right)$		$2$	$x=55°$
$\left(S\right)$		$3$	$x=105°$
$\left(R\right)$		$4$	$x=80°$

Directions: In the following question, a statement of assertion is given, followed by a corresponding statement of reason just below. Of the statements under the options, mark the correct answer.

Assertion: If two lines intersect, then the vertically opposite angles are equal.

Reason: Sum of all the angles around a point is $180°$.

Directions: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer.

Assertion: The complement of $35°$ is $55°$.

Reason: If two angles are complementary, then their sum is $90°$.

Directions: In the following questions, a statement of Assertion is given followed by a corresponding statement of Reason just below it. Of the statements, mark the correct answer.

Assertion: A line $AB$ is denoted by $\overline{AB}$.

Reason: A line has no end point.