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(a) $ {{60}^{\circ }} $

(b) $ {{70}^{\circ }} $

(c) $ {{80}^{\circ }} $

(d) $ {{90}^{\circ }} $

Answer

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Two angles are called complementary angles, if their sum is equal to one right angle i.e. 90°. Each angle is called the complement of the other. Example, 20° and 70° are complementary angles, because 30° + 60° = 90°. And,

Two angles are called supplementary angles, if their sum is equal to two right angles i.e. 180°.Each angle is called the supplement of the other. Example, 30° and 150° are supplementary angles, because 30° + 150° = 180°.

Let us suppose the complementary angle of 70° be X°, so

70°+ X° = 90°

Taking 70° to the R.H.S., we get

X° = 90° - 70°

X° = 20

we can see the figure of complementary angles,

Hence complementary angle of 70° is 20°

Now for supplementary angle of 70°,

Let us suppose the supplementary angle of 70° be Y°, so

70°+ Y° = 180°

Taking 70° to the R.H.S., we get

Y° = 180° - 70°

Y° = 110°

we can see the figure of supplementary angles,

Difference between supplement and complement = Y° - X°

=110°-20°

=90°

(180°- A°) - (90°- A°) = 180° - A° - 90° + A° = 90°

Hence the difference of supplementary and complementary angle is always 90°.