QuestionFind the complement and supplement of an angle measuring $22^{\circ} 13^{\prime}$ .

Studdy Solution

STEP 1

Assumptions1. The given angle is $22^{\circ}13^{\prime}$ . . The complement of an angle is defined as $90^{\circ}$ minus the given angle.
3. The supplement of an angle is defined as $180^{\circ}$ minus the given angle.

STEP 2

First, we need to convert the given angle to decimal form. We know that $1^{\circ}$ is equal to $60^{\prime}$ . So, we can convert $13^{\prime}$ to degrees by dividing by $60$ .
$13^{\prime} = \frac{13}{60}^{\circ}$

STEP 3

Now, we add this to the given angle to get the decimal form of the angle.
$22^{\circ}13^{\prime} =22^{\circ} + \frac{13}{60}^{\circ}$

STEP 4

Calculate the decimal form of the angle.
$22^{\circ}13^{\prime} =22^{\circ} + \frac{13}{60}^{\circ} =22.2166667^{\circ}$

STEP 5

Now, to find the complement of the angle, we subtract the angle from $90^{\circ}$ .
$Complement =90^{\circ} - Angle$

STEP 6

Plug in the value for the angle to calculate the complement.
$Complement =90^{\circ} -22.216666^{\circ}$

STEP 7

Calculate the complement of the angle.
$Complement =90^{\circ} -22.2166667^{\circ} =67.7833333^{\circ}$

STEP 8

Now, to find the supplement of the angle, we subtract the angle from $180^{\circ}$ .
$Supplement =180^{\circ} - Angle$

STEP 9

Plug in the value for the angle to calculate the supplement.
$Supplement =180^{\circ} -22.2166667^{\circ}$

STEP 10

Calculate the supplement of the angle.
$Supplement =180^{\circ} -22.2166667^{\circ} =157.7833333^{\circ}$ So, the complement of the angle $22^{\circ}13^{\prime}$ is approximately $67.78^{\circ}$ and the supplement is approximately $157.78^{\circ}$ .

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