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

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

The formula is: Complementary angle = $90^\{\backslash circ\}$ – given angle

1. Complement of $20^\{\backslash circ\}$ = $90^\{\backslash circ\}\; -\; 20^\{\backslash circ\}\; =\; 70^\{\backslash circ\}$
2. Complement of $63^\{\backslash circ\}$ = $90^\{\backslash circ\}\; -\; 63^\{\backslash circ\}\; =\; 27^\{\backslash circ\}$
3. Complement of $57^\{\backslash circ\}$ = $90^\{\backslash circ\}\; -\; 57^\{\backslash circ\}\; =\; 33^\{\backslash circ\}$

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

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 determine if a pair of angles is complementary or supplementary by finding their sum.

• If the sum of two angles is 90°, they are complementary angles.
• If the sum of two angles is 180°, they are supplementary angles.

(i) $65^\{\backslash circ\}\; +\; 115^\{\backslash circ\}\; =\; 180^\{\backslash circ\}$. These are supplementary angles.

(ii) $63^\{\backslash circ\}\; +\; 27^\{\backslash circ\}\; =\; 90^\{\backslash circ\}$. These are complementary angles.

(iii) $112^\{\backslash circ\}\; +\; 68^\{\backslash circ\}\; =\; 180^\{\backslash circ\}$. These are supplementary angles.

(iv) $130^\{\backslash circ\}\; +\; 50^\{\backslash circ\}\; =\; 180^\{\backslash circ\}$. These are supplementary angles.

(v) $45^\{\backslash circ\}\; +\; 45^\{\backslash circ\}\; =\; 90^\{\backslash circ\}$. These are complementary angles.

(vi) $80^\{\backslash circ\}\; +\; 10^\{\backslash circ\}\; =\; 90^\{\backslash circ\}$. These are complementary angles.

Let the angle be $x$. If an angle is equal to its complement, it means the angle and its complement have the same measure. Since complementary angles add up to 90°, we can write the equation:

$x\; +\; x\; =\; 90^\{\backslash circ\}$

Combining the terms:

$2x\; =\; 90^\{\backslash circ\}$

To find the value of $x$, divide both sides by 2:

$$x\; =\; \backslash frac\{90^\{\backslash circ\}\}\{2\}\; =\; 45^\{\backslash circ\}$$

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 the angle and its supplement have the same measure. Since supplementary angles add up to 180°, we can write the equation:

$x\; +\; x\; =\; 180^\{\backslash circ\}$

Combining the terms:

$2x\; =\; 180^\{\backslash circ\}$

To find the value of $x$, divide both sides by 2:

$x\; =\; \backslash frac\{180^\{\backslash circ\}\}\{2\}\; =\; 90^\{\backslash circ\}$

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