Question

name sudan
e is the mid - point of df. find the segment lengths.

1. find de and ef.

26
d e f

1. find de and df.

11
d e f
b is the mid - point of ac.

1. find the value of x.

4x 36
a b c
\\(\overrightarrow{bd}\\) bisects \\(\angle abc\\). find the angle measure.

1. find \\(\angle abd\\).

24°
a d b c

1. find \\(\angle dbc\\).

116°
a d b c

Explanation:

Step1: Use mid - point property for segment lengths

Since E is the mid - point of DF and DF = 26, then DE=EF. So DE = $\frac{26}{2}=13$ and EF = 13.

Step2: Use mid - point property for segment lengths

Since E is the mid - point of DF and EF = 11, then DE = EF = 11 and DF=DE + EF=11 + 11 = 22.

Step3: Use mid - point property for segment lengths

Since B is the mid - point of AC, then AB = BC. So 4x=36, and x = $\frac{36}{4}=9$.

Step4: Use angle - bisector property

Since $\overrightarrow{BD}$ bisects $\angle ABC$ and $\angle DBC = 24^{\circ}$, then $\angle ABD=\angle DBC = 24^{\circ}$.

Step5: Use angle - bisector property

Since $\overrightarrow{BD}$ bisects $\angle ABC$ and $\angle ABC=116^{\circ}$, then $\angle DBC=\frac{116^{\circ}}{2}=58^{\circ}$.

Answer:

1. DE = 13

EF = 13

1. DE = 11

DF = 22

1. x = 9
2. $\angle ABD = 24^{\circ}$
3. $\angle DBC = 58^{\circ}$