Question

Find the complement of the angle :$\frac{1}{4}$ of a right angle.

• A. $67\cdot 5^o$
• B. $57\cdot 5^o$
• C. $37\cdot 5^o$
• D. none of the above

Answer 1

The correct option is

A

$67\cdot 5^o$

We know, two angles are complementary when they add up to ${90}^o.$

Given, measure of one fourth of right angle is $=\frac{1}{4}\times {90}^o={\frac{45}{2}}^o.$

$\Rightarrow$ Measure of other complementary angle $={90}^o-$ ${\frac{45}{2}}^o$ $={\frac{180-45}{2}}^o$$={\frac{135}{2}}^o$ $={67.5}^o.$

$\therefore$ Measure of a complementary angle of $\frac{1}{4}$ of a right angle $={67.5}^o$.