Question

Find the complement of: ${58}^{\circ }{20}^{\prime }{25}^{\prime \prime }$.

Answer 1

We know, two angles are said to be complementary, if the sum of their measures is ${90}^{\circ }.$

Let the angle be $x^{\circ }$ and its complement is ${90}^{\circ }-x^{\circ }$

We can write, ${90}^{\circ }={89}^{\circ }{59}^{\prime }{60}^{\prime \prime }$.

Then, the complement of $x={58}^{\circ }{20}^{\prime }{25}^{\prime \prime }$

$={90}^{\circ }-x^{\circ }$

$={90}^{\circ }-{58}^{\circ }{20}^{\prime }{25}^{\prime \prime }$

$={89}^{\circ }{59}^{\prime }{60}^{\prime \prime }-{58}^{\circ }{20}^{\prime }{25}^{\prime \prime }$

$={31}^{\circ }{39}^{\prime }{35}^{\prime \prime }$.

Hence, the complement is ${31}^{\circ }{39}^{\prime }{35}^{\prime \prime }$.