teacher :
find the missing angle measurement using the angle addition postulate.
1)
$ \angle e f h=67^{\circ} $
$ \angle h f g=43^{\circ} $
$ \angle e f g= $
2)
$ \angle m n p= $
$ \angle p n o=40^{\circ} $
$ \angle m n o=150^{\circ} $
3)
$ \angle g h k=80^{\circ} $
$ \angle k h j= $
$ \angle g h j=105^{\circ} $
4)
$ \angle q r t=98^{\circ} $
$ \angle t r s=17^{\circ} $
$ \angle q r s= $
5)
$ \angle k l n=62^{\circ} $
$ \angle n l m= $
$ \angle k l m=125^{\circ} $
6)
$ \angle d e g= $
$ \angle g e f=28^{\circ} $
$ \angle d e f=160^{\circ} $
7)
$ \angle b c e=122^{\circ} $
$ \angle e c d= $
$ \angle b c d=145^{\circ} $
8)
$ \angle c d f= $
$ \angle f d e=41^{\circ} $
$ \angle c d e=120^{\circ} $
9)
$ \angle f g j=101^{\circ} $
$ \angle j g h=34^{\circ} $
$ \angle f g h= $

Question

Accepted Answer

# Explanation:
## 1)
### Step1: Use angle addition postulate
The angle addition postulate states that if we have two adjacent angles $\angle EFH$ and $\angle HFG$, then $\angle EFG=\angle EFH + \angle HFG$
### Step2: Substitute the given values
Given $\angle EFH = 67^{\circ}$ and $\angle HFG=43^{\circ}$, then $\angle EFG=67^{\circ}+ 43^{\circ}$
$$
\begin{align*}
\angle EFG&=67 + 43\
&=110^{\circ}
\end{align*}
$$

## 2)
### Step1: Use angle addition postulate
By the angle addition postulate, $\angle MNO=\angle MNP+\angle PNO$
### Step2: Solve for $\angle MNP$
We know $\angle MNO = 150^{\circ}$ and $\angle PNO=40^{\circ}$. Then $\angle MNP=\angle MNO-\angle PNO$
$$
\begin{align*}
\angle MNP&=150^{\circ}- 40^{\circ}\
&=110^{\circ}
\end{align*}
$$

## 3)
### Step1: Use angle addition postulate
By the angle addition postulate, $\angle GHJ=\angle GHK+\angle KHJ$
### Step2: Solve for $\angle KHJ$
We know $\angle GHJ = 105^{\circ}$ and $\angle GHK=80^{\circ}$. Then $\angle KHJ=\angle GHJ-\angle GHK$
$$
\begin{align*}
\angle KHJ&=105^{\circ}- 80^{\circ}\
&=25^{\circ}
\end{align*}
$$

## 4)
### Step1: Use angle addition postulate
By the angle addition postulate, $\angle QRS=\angle QRT+\angle TRS$
### Step2: Substitute the given values
Given $\angle QRT = 98^{\circ}$ and $\angle TRS=17^{\circ}$, then $\angle QRS=98^{\circ}+ 17^{\circ}$
$$
\begin{align*}
\angle QRS&=98 + 17\
&=115^{\circ}
\end{align*}
$$

## 5)
### Step1: Use angle addition postulate
By the angle addition postulate, $\angle KLM=\angle KLN+\angle NLM$
### Step2: Solve for $\angle NLM$
We know $\angle KLM = 125^{\circ}$ and $\angle KLN=62^{\circ}$. Then $\angle NLM=\angle KLM-\angle KLN$
$$
\begin{align*}
\angle NLM&=125^{\circ}- 62^{\circ}\
&=63^{\circ}
\end{align*}
$$

## 6)
### Step1: Use angle addition postulate
By the angle addition postulate, $\angle DEF=\angle DEG+\angle GEF$
### Step2: Solve for $\angle DEG$
We know $\angle DEF = 160^{\circ}$ and $\angle GEF=28^{\circ}$. Then $\angle DEG=\angle DEF-\angle GEF$
$$
\begin{align*}
\angle DEG&=160^{\circ}- 28^{\circ}\
&=132^{\circ}
\end{align*}
$$

## 7)
### Step1: Use angle addition postulate
By the angle addition postulate, $\angle BCD=\angle BCE+\angle ECD$
### Step2: Solve for $\angle ECD$
We know $\angle BCD = 145^{\circ}$ and $\angle BCE=122^{\circ}$. Then $\angle ECD=\angle BCD-\angle BCE$
$$
\begin{align*}
\angle ECD&=145^{\circ}- 122^{\circ}\
&=23^{\circ}
\end{align*}
$$

## 8)
### Step1: Use angle addition postulate
By the angle addition postulate, $\angle CDE=\angle CDF+\angle FDE$
### Step2: Solve for $\angle CDF$
We know $\angle CDE = 120^{\circ}$ and $\angle FDE=41^{\circ}$. Then $\angle CDF=\angle CDE-\angle FDE$
$$
\begin{align*}
\angle CDF&=120^{\circ}- 41^{\circ}\
&=79^{\circ}
\end{align*}
$$

## 9)
### Step1: Use angle addition postulate
By the angle addition postulate, $\angle FGH=\angle FGJ+\angle JGH$
### Step2: Substitute the given values
Given $\angle FGJ = 101^{\circ}$ and $\angle JGH=34^{\circ}$, then $\angle FGH=101^{\circ}+ 34^{\circ}$
$$
\begin{align*}
\angle FGH&=101 + 34\
&=135^{\circ}
\end{align*}
$$

# Answer:
1. $\angle EFG = 110^{\circ}$
2. $\angle MNP = 110^{\circ}$
3. $\angle KHJ = 25^{\circ}$
4. $\angle QRS = 115^{\circ}$
5. $\angle NLM = 63^{\circ}$
6. $\angle DEG = 132^{\circ}$
7. $\angle ECD = 23^{\circ}$
8. $\angle CDF = 79^{\circ}$
9. $\angle FGH = 135^{\circ}$

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QUESTION IMAGE

Question

Explanation:

1)

Step1: Use angle addition postulate

Step2: Substitute the given values

2)

Step1: Use angle addition postulate

Step2: Solve for \(\angle MNP\)

3)

Step1: Use angle addition postulate

Step2: Solve for \(\angle KHJ\)

4)

Step1: Use angle addition postulate

Step2: Substitute the given values

5)

Step1: Use angle addition postulate

Step2: Solve for \(\angle NLM\)

6)

Step1: Use angle addition postulate

Step2: Solve for \(\angle DEG\)

7)

Step1: Use angle addition postulate

Step2: Solve for \(\angle ECD\)

8)

Step1: Use angle addition postulate

Step2: Solve for \(\angle CDF\)

9)

Step1: Use angle addition postulate

Step2: Substitute the given values

Answer: