m is the mid - point of the segment. find the segment lengths.
1. find am and mc.
2. find mt and rt.
find the coordinates of the mid - point of km.
3. (-3,2)m (-3,-4)k
4. m(4,1) k(2,-3)
st bisects ∠rsu. find the angle measures.
5. find m∠rst and m∠tsu.
6. find m∠tsu and m∠rsu.
bd bisects ∠abc. find the value of the variable.
7. 88° 3x°
8. 56° (y + 10)°
determine whether the angles are complementary, supple -

Question

Accepted Answer

1.
# Explanation:
## Step1: Recall mid - point property
Since $M$ is the mid - point of segment $AC$ and $AC = 28$, then $AM=MC=\frac{AC}{2}$.
## Step2: Calculate segment lengths
$AM = MC=\frac{28}{2}=14$
# Answer:
$AM = 14$, $MC = 14$

2.
# Explanation:
## Step1: Recall mid - point property
Since $M$ is the mid - point of segment $RT$ and $RM = 20.5$, then $MT=RM$ and $RT = 2RM$. So $MT = 20.5$ and $RT=2\times20.5 = 41$
# Answer:
$MT = 20.5$, $RT = 41$

3.
# Explanation:
## Step1: Use mid - point formula
The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $K(-3,-4)$ and $M(-3,2)$, so $x_1=-3,y_1=-4,x_2=-3,y_2 = 2$.
## Step2: Calculate coordinates
$x=\frac{-3+( - 3)}{2}=\frac{-6}{2}=-3$, $y=\frac{-4 + 2}{2}=\frac{-2}{2}=-1$. The mid - point is $(-3,-1)$
# Answer:
$(-3,-1)$

4.
# Explanation:
## Step1: Use mid - point formula
The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here $K(2,-3)$ and $M(4,1)$, so $x_1 = 2,y_1=-3,x_2 = 4,y_2=1$.
## Step2: Calculate coordinates
$x=\frac{2 + 4}{2}=\frac{6}{2}=3$, $y=\frac{-3+1}{2}=\frac{-2}{2}=-1$. The mid - point is $(3,-1)$
# Answer:
$(3,-1)$

5.
# Explanation:
## Step1: Recall angle - bisector property
Since $\overrightarrow{ST}$ bisects $\angle RSU$ and $\angle RSU=78^{\circ}$, then $\angle RST=\angle TSU=\frac{\angle RSU}{2}$
## Step2: Calculate angle measures
$\angle RST=\angle TSU=\frac{78^{\circ}}{2}=39^{\circ}$
# Answer:
$m\angle RST = 39^{\circ}$, $m\angle TSU=39^{\circ}$

6.
# Explanation:
## Step1: Recall angle - bisector property
Since $\overrightarrow{ST}$ bisects $\angle RSU$ and $\angle RST = 49^{\circ}$, then $\angle TSU=\angle RST = 49^{\circ}$ and $\angle RSU=2\angle RST$
## Step2: Calculate angle measures
$\angle TSU = 49^{\circ}$, $\angle RSU=2\times49^{\circ}=98^{\circ}$
# Answer:
$m\angle TSU = 49^{\circ}$, $m\angle RSU=98^{\circ}$

7.
# Explanation:
## Step1: Recall angle - bisector property
Since $\overrightarrow{BD}$ bisects $\angle ABC$, then $\angle ABD=\angle DBC$. So $3x=66$
## Step2: Solve for $x$
Divide both sides of the equation $3x = 66$ by 3: $x=\frac{66}{3}=22$
# Answer:
$x = 22$

8.
# Explanation:
## Step1: Recall angle - bisector property
Since $\overrightarrow{BD}$ bisects $\angle ABC$, then $\angle ABD=\angle DBC$. So $y + 10=56$
## Step2: Solve for $y$
Subtract 10 from both sides of the equation: $y=56 - 10=46$
# Answer:
$y = 46$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall mid - point property

Step2: Calculate segment lengths

Step1: Recall mid - point property

Step1: Use mid - point formula

Step2: Calculate coordinates

Answer: