Question

find the complementary and supplementary angles. 22°2613 the complementary angle is □°□□. the supplementary angle is □°□□.

Explanation:

Step1: Recall angle - relation formulas

Complementary angle of $\theta$ is $90^{\circ}-\theta$, supplementary angle of $\theta$ is $180^{\circ}-\theta$.

Step2: Convert $90^{\circ}$ for subtraction

$90^{\circ}=89^{\circ}59'60''$.

Step3: Calculate the complementary angle

$89^{\circ}59'60'' - 22^{\circ}26'13''=(89 - 22)^{\circ}+(59 - 26)'+(60 - 13)''=67^{\circ}33'47''$.

Step4: Convert $180^{\circ}$ for subtraction

$180^{\circ}=179^{\circ}59'60''$.

Step5: Calculate the supplementary angle

$179^{\circ}59'60'' - 22^{\circ}26'13''=(179 - 22)^{\circ}+(59 - 26)'+(60 - 13)''=157^{\circ}33'47''$.

Answer:

The complementary angle is $67^{\circ}33'47''$.
The supplementary angle is $157^{\circ}33'47''$.