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

Complementary angles are two angles that add up to 90 degrees. To find the complement of a given angle, we subtract the angle from 90 degrees.

The formula is: Complementary Angle = $90^\{\backslash circ\}$ – Given Angle

1. Complement of $63^\{\backslash circ\}$ = $90^\{\backslash circ\}\; -\; 63^\{\backslash circ\}\; =\; 27^\{\backslash circ\}$
2. Complement of $57^\{\backslash circ\}$ = $90^\{\backslash circ\}\; -\; 57^\{\backslash circ\}\; =\; 33^\{\backslash circ\}$

Supplementary angles are two angles that add up to 180 degrees. To find the supplement of a given angle, we subtract the angle from 180 degrees.

The formula is: Supplementary Angle = $180^\{\backslash circ\}$ – Given Angle

1. Supplement of $105^\{\backslash circ\}$ = $180^\{\backslash circ\}\; -\; 105^\{\backslash circ\}\; =\; 75^\{\backslash circ\}$
2. Supplement of $87^\{\backslash circ\}$ = $180^\{\backslash circ\}\; -\; 87^\{\backslash circ\}\; =\; 93^\{\backslash circ\}$
3. Supplement of $154^\{\backslash circ\}$ = $180^\{\backslash circ\}\; -\; 154^\{\backslash circ\}\; =\; 26^\{\backslash circ\}$

We need to check the sum of each pair of angles to determine if they are complementary (sum = 90°) or supplementary (sum = 180°).

1. $65^\{\backslash circ\}\; +\; 115^\{\backslash circ\}\; =\; 180^\{\backslash circ\}$. Since the sum is 180°, these angles are supplementary.
2. $63^\{\backslash circ\}\; +\; 27^\{\backslash circ\}\; =\; 90^\{\backslash circ\}$. Since the sum is 90°, these angles are complementary.
3. $112^\{\backslash circ\}\; +\; 68^\{\backslash circ\}\; =\; 180^\{\backslash circ\}$. Since the sum is 180°, these angles are supplementary.
4. $130^\{\backslash circ\}\; +\; 50^\{\backslash circ\}\; =\; 180^\{\backslash circ\}$. Since the sum is 180°, these angles are supplementary.
5. $45^\{\backslash circ\}\; +\; 45^\{\backslash circ\}\; =\; 90^\{\backslash circ\}$. Since the sum is 90°, these angles are complementary.
6. $80^\{\backslash circ\}\; +\; 10^\{\backslash circ\}\; =\; 90^\{\backslash circ\}$. Since the sum is 90°, these angles are complementary.

Let the angle be $x$. If an angle is equal to its complement, it means that the angle and its complement add up to 90 degrees, and the angle itself is half of that sum.

So, we can write the equation: $x\; +\; x\; =\; 90^\{\backslash circ\}$

This simplifies to: $2x\; =\; 90^\{\backslash circ\}$

Dividing both sides by 2, we get: $x\; =\; \backslash frac\{90^\{\backslash circ\}\}\{2\}\; =\; 45^\{\backslash circ\}$

Therefore, the angle that is equal to its complement is 45°.

Let the angle be $x$. If an angle is equal to its supplement, it means that the angle and its supplement add up to 180 degrees, and the angle itself is half of that sum.

We can set up the equation: $x\; +\; x\; =\; 180^\{\backslash circ\}$

This simplifies to: $2x\; =\; 180^\{\backslash circ\}$

Dividing both sides by 2, we find: $x\; =\; \backslash frac\{180^\{\backslash circ\}\}\{2\}\; =\; 90^\{\backslash circ\}$

Thus, the angle that is equal to its supplement is 90°.