Elaborating Adjacent angles definition:

As given in definition of adjacent angles above, the same side we are talking about is ob here and the vertex is point o.

adjacent_angles_defenition

Thus according to adjacent angles definition, ∠aob and ∠bod are adjacent to each other with side ob being common to both.

Significance of adjacent angles in real life:

There is lot of significance of adjacent angles in real life. You can find the concept of adjacent angles in analog clocks between minute, hour and second hands as shown below. Similar real life examples can be found in every small things that makes you believe that maths is everywhere.

angles_time

What are adjacent complementary angles?

The adjacent angles whose sum is equal to 90° are known as adjacent complementary angles. As shown in below figure, ∠a + ∠b = 90° which makes them adjacent as well as complementary.

adjacent_complem_angles

What are adjacent supplementary angles?

The adjacent angles whose sum is equal to 180° are known as adjacent supplementary angles. As shown in below figure, ∠a + ∠b = 180° which makes them adjacent as well as complementary.

adjacent_suplem_angles

Lets have examples of adjacent angles:

A couple of examples of adjacent angles will make the concept clear.

(i) If ∠a = 30° and ∠b is adjacent as well as complementary to a, find b:

As we know both angles a and b are adjacent and complementary, ∠a + ∠b = 90° which gives

∠b = 90 – 30 = 60°.

(ii) If ∠a = 50° and ∠b is adjacent as well as supplementary to a, find b:

As we know both angles a and b are adjacent and supplementary, ∠a + ∠b = 180° which gives

∠b = 180 – 50 = 130°.

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