CBSE Class 7 Maths NCERT Solutions: Chapter 5 Lines and Angles

The angle formed between the North direction and the West direction is a right angle, measuring 90°. Similarly, the angle formed between the South direction and the East direction is also a right angle, measuring 90°.

When we consider these two angles together, their sum is 90° + 90° = 180°.

Angles that add up to 180° are known as supplementary angles.

Therefore, the angles between North and West and South and East are supplementary.

Hence, the correct option is (b).

The angle formed between the South direction and the West direction is a right angle, measuring 90°. The angle formed between the South direction and the East direction is also a right angle, measuring 90°.

These two angles share a common vertex (South) and a common arm (the line pointing South). Their non-common arms point West and East, which are in opposite directions, forming a straight line.

When two adjacent angles share a common vertex and a common arm, and their non-common arms form a straight line, they form a linear pair. The sum of angles in a linear pair is always 180°.

Therefore, the angles between South and West and South and East are making a linear pair.

Hence, the correct option is (c).

According to the law of reflection, the angle of incidence is equal to the angle of reflection. In this scenario, angle ABP is the angle of incidence, and angle CBQ (which is vertically opposite to ABP) is the angle of reflection. However, the problem statement implies that the angle between the incident ray and the reflected ray is given, and we need to find the angle between the incident ray and the mirror.

Let's assume that the angle of incidence is equal to the angle of reflection. Let $\angle ABP = \angle CBQ$. We are given $\angle ABC = 46^{\circ}$.

Since PQ is a straight line (the mirror), the angles on this line at point B must sum to 180°.

So, we have the equation: $\angle ABP + \angle ABC + \angle CBQ = 180^{\circ}$

Since $\angle ABP = \angle CBQ$, we can substitute $\angle ABP$ for $\angle CBQ$:

$\angle ABP + 46^{\circ} + \angle ABP = 180^{\circ}$

Combine the like terms:

$2 \angle ABP + 46^{\circ} = 180^{\circ}$

Subtract 46° from both sides:

$2 \angle ABP = 180^{\circ} - 46^{\circ}$

$2 \angle ABP = 134^{\circ}$

Divide by 2 to find the measure of $\angle ABP$:

$\angle ABP = \frac{134^{\circ}}{2}$

$\angle ABP = 67^{\circ}$

Hence, the correct option is (b).

Let the unknown angle be represented by the variable $x$. The complement of an angle is defined as the angle that, when added to the original angle, sums up to 90°.

According to the problem statement, the complement of the angle $x$ is 79°. This can be written as an equation:

$90^{\circ} - x = 79^{\circ}$

To find the value of $x$, we rearrange the equation:

$x = 90^{\circ} - 79^{\circ}$

Performing the subtraction:

$x = 11^{\circ}$

Therefore, the measure of the required angle is 11°.

Hence, the correct option is (b).

Vertically opposite angles are formed when two lines intersect, and they are always equal. Let's denote the measure of each vertically opposite angle as $x$.

The problem states that these angles are also supplementary, meaning their sum is 180°.

So, we can write the equation: $x + x = 180^{\circ}$

Combining the terms:

$2x = 180^{\circ}$

Solving for $x$ by dividing both sides by 2:

$x = \frac{180^{\circ}}{2}$

$x = 90^{\circ}$

This means that each of the vertically opposite angles must measure 90°. Therefore, the angles are 90° and 90°.

Hence, the correct option is (b).

Angles that form a linear pair are adjacent angles whose non-common sides are opposite rays, meaning they lie on a straight line. The sum of angles in a linear pair is always 180°.

Let the unknown angle that forms a linear pair with 61° be represented by $x$.

We can set up the equation based on the property of linear pairs:

$x + 61^{\circ} = 180^{\circ}$

To find the value of $x$, subtract 61° from both sides of the equation:

$x = 180^{\circ} - 61^{\circ}$

Performing the subtraction:

$x = 119^{\circ}$

Therefore, the angle that makes a linear pair with 61° is 119°.

Hence, the correct option is (d).

To determine the relationship between the angles $x$ and $90^{\circ} - x$, we need to find their sum.

Sum = $x + (90^{\circ} - x)$

When we simplify this expression, the $x$ terms cancel out:

Sum = $x - x + 90^{\circ}$

Sum = $90^{\circ}$

By definition, two angles are complementary if their sum is 90°.

Therefore, the angles $x$ and $90^{\circ} - x$ are complementary.

Hence, the correct option is (b).