part b
given: $ \triangle efg \cong \triangle rst $ find each value below.
6. $ m\angle f= $
7. $ y= $
8. $ x= $
9. $ st= $

Question

Accepted Answer

# Explanation:
## Step1: Find $m\angle F$
Since $\triangle EFG\cong\triangle RST$, corresponding angles are equal. In $\triangle EFG$, using the angle - sum property of a triangle ($m\angle E + m\angle F+m\angle G=180^{\circ}$). Given $m\angle E=(4x + 6)^{\circ}$, $m\angle G = 28^{\circ}$, and in right - angled triangle $\triangle RST$, $m\angle R = 90^{\circ}$. Corresponding to $\angle R$ is $\angle F$ (because of congruence). So $m\angle F=90^{\circ}-28^{\circ}=62^{\circ}$

## Step2: Find $z$
Since $\triangle EFG\cong\triangle RST$, corresponding sides are equal. So $3z−8=z + 4$
$$
\begin{align*}
3z−z&=4 + 8\
2z&=12\
z&=6
\end{align*}
$$

## Step3: Find $y$
Since $\triangle EFG\cong\triangle RST$, corresponding angles are equal. $\angle E$ corresponds to $\angle T$. $m\angle E=(4x + 6)^{\circ}$, $m\angle T=(5y−2)^{\circ}$. First, in $\triangle EFG$, $m\angle E=90^{\circ}-28^{\circ}=62^{\circ}$. Then $5y−2 = 62$
$$
\begin{align*}
5y&=62 + 2\
5y&=64\
y&=12.8
\end{align*}
$$

## Step4: Find $x$
Since $m\angle E=(4x + 6)^{\circ}$ and $m\angle E = 62^{\circ}$ (from congruence and angle - sum property). Then $4x+6=62$
$$
\begin{align*}
4x&=62-6\
4x&=56\
x&=14
\end{align*}
$$

## Step5: Find $ST$
Since $z = 6$ and $ST=z + 4$, then $ST=6 + 4=10$

# Answer:
6. $m\angle F = 62^{\circ}$
7. $y = 12.8$
8. $x = 14$
9. $ST = 10$

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QUESTION IMAGE

Question

Explanation:

Step1: Find \(m\angle F\)

Step2: Find \(z\)

Step3: Find \(y\)

Step4: Find \(x\)

Step5: Find \(ST\)

Answer: