case /data -based (4 Marks)

Question 14 Marks

Three lines shown in the igure intersect each other at point $P.$

Line lis perpendicular to line n.
The measure of $\angle 2$ is $65^\circ .$
$1.$ What is the measure of $\angle 6?$
$2.$ What is the sum of the measure of $\angle 3$ and $\angle 4?$
$A. 95^\circ $
$B. 115^\circ $
$C. 120^\circ $
$D. 155^\circ $

Answer

$9. 25^\circ $
$10. B. 115^\circ $

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Question 24 Marks

A diagram of a see-saw is given below.

$1.$ State all the pairs of vertically opposite angles in the given figure.
$2.$ Which of the following is a pair of alternate exterior angles?
$A. \angle 1$ and $\angle 4$
$B. \angle 2$ and $\angle 8$
$C. \angle 3$ and $\angle 8$
$D. \angle 4$ and $\angle 6$

Answer

$7. \angle 1, \angle 4$
$\angle 2, \angle 3$
$\angle 5, \angle 7$
$\angle 6, \angle 8$
$8. B. \angle 2$ and $\angle 8$

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Question 34 Marks

In the igure given below, $AD$ is a straight line. $PS$ and $QR$ are perpendicular to $AD$.
$GH$ is parallel to $IJ$ and $KL$ is parallel to $MN.$

$1.$ What type of angles are $\angle r$ and $\angle t?$
$A.$ Adjacent angles
$B.$ Vertically opposite
$C.$ Corresponding angles
$D.$ Alternate exterior angles
$2.$ The measure of $\angle s = 120^\circ .$
What is the measure of $\angle t?$
$A. 30^\circ $
$B. 60^\circ $
$C. 90^\circ $
$D. 120^\circ $
$3.$ What is the measure of $\angle x?$
$A. 45^\circ $
$B. 60^\circ $
$C. 90^\circ $
$D. 120^\circ $
$4.$ Why are the lines $SP$ and $RQ$ parallel to each other$?$
$5.$ Is $DF$ transversal to $KL$ and $MN?$ Give reason.
$6.$ Which of the following is true for $DE$ and $DF?$
$A.$ They are parallel
$B.$ They intersect at $A$
$C.$ They intersect at $D$
$D.$ They have $AD$ as transversal

Answer

$1. C.$ Corresponding angles
$2. B. 60^\circ $
$3. C. 90^\circ $
$4.$ Reasoning involves the condition: When two lines are perpendicular to a
line, they are parallel to each other.
● $SP$ and $QR$ are perpendicular to $AD,$ so they are parallel to each other.
$5.$ Yes, reasoning involves the deinition of transversal line.
● Yes, $DF$ is transversal to $KL$ and $MN$ because it cuts the parallel lines $KL$ and $MN.$
● Yes, $DF$ is transversal to $KL$ and $MN$ because it intersects two lines at distinct points.
$6. C.$ They intersect at $D$

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Maths case /data -based (4 Marks)

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