Question

Find the measures of a compliment and a supplement of $\angle K$.

$m\angle K=72\frac{1}{2}$

Short answer

The measures of a compliment and a supplement of $\angle K$are $17\frac{1}{2}$and $107\frac{1}{2}$ respectively.

Step-by-step solution

Step 1. Formula to find the compliment and supplement of the angle K.

The complement of the angle K is given by:

$m\left\{comp.\angle K\right\}=90-K$

The supplement of the angle K is given by:

$m\left\{\mathrm{supp}.\angle K\right\}=180-K$

Step 2. Find the complement of the angle K by substituting for K into the formula.

$m\left\{comp.\angle K\right\}=90-72\frac{1}{2}$

$=17\frac{1}{2}$

Therefore, the complement of the angle K is $=17\frac{1}{2}$.

Step 3. Find the supplement of the angle K by substituting for K into the formula.

$m\left\{\mathrm{supp}.\angle K\right\}=180-72\frac{1}{2}$

$=107\frac{1}{2}$

Therefore, the supplement of the angle K is $107\frac{1}{2}$.