CLASS-6
SUPPLEMENTARY ANGLE

SUPPLEMENTARY ANGLE -

Supplementary angles are a pair of angles whose measures add up to 180∘. In other words, if you have two angles A and B such that A + B = 180∘, then A and B are supplementary angles.

Mathematically, if A and B are supplementary angles, we write:

A + B = 180∘

Here are some key points about supplementary angles:

  1. Sum of Measures:- The sum of the measures of supplementary angles is always 180∘.
  2. Examples:-  60∘ and 120∘ are supplementary angles because 60∘ + 120∘ = 180∘. 90∘ and 90∘ are also supplementary because 90∘ + 90∘ = 180∘.
  3. Straight Line:- Supplementary angles are often associated with a straight line. If two angles form a straight line, they are supplementary.
  4. Symbolically:- If A and B are supplementary angles, we can express this relationship as A ∥ B, where ∥ represents parallel lines.
  5. Supplementary Pairs:- Supplementary angles form pairs, and each angle in the pair supplements the other.
  6. Complementary vs. Supplementary:- The main difference between complementary and supplementary angles is the sum they make. Complementary angles add up to 90∘, while supplementary angles add up to 180∘.


geometry

In figure (i), 

∠ABC + ∠DEF = 130° + 50° = 180°

So, sum of their measures is 180°, therefore ∠ABC & ∠DEF are supplementary.


In figure (ii),

∠ABC + ∠DEF = 105° + 65° = 170°

So, sum of their measures is not 180°, therefore ∠ABC & ∠DEF are not supplementary.


Example.1) Find the Supplement of the angle 1/3 of 210°. 

Ans.)

Step 1:- Convert 1/3 of 210° That is, 1/3 x 210° = 70°

Step 2:- Supplement of 70° = 180° – 70° = 110° Therefore, Supplement of the angle 1/3 of 210° is 110°.    (Ans.)


Example.2) The measures of two angles are (x + 25)° and (3x + 15)°. Find the value of x if angles are supplementary angles.

Ans.) We know that, Sum of Supplementary angles = 180 degrees So,

(x + 25)° + (3x + 15)° = 180°

4x + 40° = 180°

4x = 140°

x = 35°

The value of x is 35 degrees.    (Ans.)

Understanding supplementary angles is important in geometry, especially when dealing with parallel lines and transversals, as well as when studying angles formed by intersecting lines and shapes.