Question 129

If the compliment of an angle is one-fourth of its supplementary angle, then the angle is

Solution

Let the angle be A

Complement of an angle with A is given by $$(90^{\circ} -A)$$

Supplement of an angle with A is given by $$(180^{\circ} - A)$$

Now equation can be written as,

$$90^{\circ} - A$$ = $$\frac{1}{4} (180^{\circ} - A)$$

$$90^{\circ} - A$$ = $$(45^{\circ} - \frac{A}{4})$$

$$A(1 - \frac{1}{4}) = 45^{\circ}$$

$$A = 60^{\circ}$$

Hence, option B is the correct answer.

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