angle complements and supplements
write the complements of these angles.
55. 86°1948
57. 44°34
write the supplements of these angles.
59. 109°56
61. 178°921

Question

Accepted Answer

# Explanation:
## Step1: Recall the formula for complement
The complement of an angle $A$ is $90^{\circ}-A$.
## Step2: Calculate the complement of $86^{\circ}19'48''$
$$
\begin{align*}
90^{\circ}&=89^{\circ}59'60''\
90^{\circ}- 86^{\circ}19'48''&=(89^{\circ}-86^{\circ})+(59'-19')+(60'' - 48'')\
&=3^{\circ}40'12''
\end{align*}
$$
## Step3: Calculate the complement of $44^{\circ}3'4''$
$$
\begin{align*}
90^{\circ}&=89^{\circ}59'60''\
90^{\circ}-44^{\circ}3'4''&=(89^{\circ}-44^{\circ})+(59'-3')+(60'' - 4'')\
&=45^{\circ}56'56''
\end{align*}
$$
## Step4: Recall the formula for supplement
The supplement of an angle $B$ is $180^{\circ}-B$.
## Step5: Calculate the supplement of $109^{\circ}56'$
$$
\begin{align*}
180^{\circ}&=179^{\circ}60'\
180^{\circ}-109^{\circ}56'&=(179^{\circ}-109^{\circ})+(60'-56')\
&=70^{\circ}4'
\end{align*}
$$
## Step6: Calculate the supplement of $178^{\circ}9'21''$
$$
\begin{align*}
180^{\circ}&=179^{\circ}59'60''\
180^{\circ}-178^{\circ}9'21''&=(179^{\circ}-178^{\circ})+(59'-9')+(60'' - 21'')\
&=1^{\circ}50'39''
\end{align*}
$$

# Answer:
- Complement of $86^{\circ}19'48''$: $3^{\circ}40'12''$
- Complement of $44^{\circ}3'4''$: $45^{\circ}56'56''$
- Supplement of $109^{\circ}56'$: $70^{\circ}4'$
- Supplement of $178^{\circ}9'21''$: $1^{\circ}50'39''$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for complement

Step2: Calculate the complement of \(86^{\circ}19'48''\)

Step3: Calculate the complement of \(44^{\circ}3'4''\)

Step4: Recall the formula for supplement

Step5: Calculate the supplement of \(109^{\circ}56'\)

Step6: Calculate the supplement of \(178^{\circ}9'21''\)

Answer: