Complementary & Supplementary Angles

byDecode Entrance Exam -April 23, 2021

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Two angles are called complementary if their measures add to 90 degrees, and called supplementary if their measures add to 180 degrees.

Example Question

An angle is equal to two-third of its supplements. Find its measure.

Ans.

Let x and y be the two angles

They are supplement means $x + y = 180$ $^{\circ}$

Now one angle is two third of another which

means $x = 2 y / 3$

putting in to equation

$\frac{2 y}{3} + y = 18 0^{\circ}$

$\Rightarrow \frac{2 y + 3 y}{3} = 18 0^{\circ}$

$\Rightarrow 5 y = 180 \times 3$

$\Rightarrow y = \frac{1 8 0 \times 3}{5}$

$\Rightarrow y = 108$

$y = 108$

$x = \frac{2 y}{3} = \frac{2 \cdot 1 0 8}{3} = 72$

$∴ x = 72$ and $y = 108$

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