Question

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

$m\angle A=75$

Short answer

The measures of a complement and a supplement of $\angle A$are 15 and 105 respectively.

Step-by-step solution

Step 1. Formula to find the complement and supplement of the angle A.

The complement of the angle A is given by:

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

The supplement of the angle A is given by:

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

Step 2. Find the complement of the angle A by substituting 75 for A into the formula.

$m\left\{comp.\angle A\right\}=90-75$

$=15$

Therefore, the complement of angle A is 15.

Step 3. Find the supplement of the angle A by substituting 75 for A into the formula.

$m\left\{\mathrm{supp}.\angle A\right\}=180-75$

$=105$

Therefore, the supplement of angle A is 105.