Question

1. what is another name for ∠cad?

example 2

1. in the figure, $overrightarrow{lf}$ and $overrightarrow{lk}$ are opposite rays. $overrightarrow{lg}$ bisects ∠flh. if $mangle flg=(14x + 5)^{circ}$ and $mangle hlg=(17x - 1)^{circ}$, find $mangle flh$.

Explanation:

Step1: Recall angle - naming convention

An angle can be named by the vertex letter in the middle of three - point notation. $\angle CAD$ can also be named $\angle DAC$ since the vertex is point $A$ and the rays are $\overrightarrow{AC}$ and $\overrightarrow{AD}$.

Step2: Use angle - bisector property for second part

Since $\overrightarrow{LG}$ bisects $\angle FLH$, then $m\angle FLG=m\angle HLG$.
Set up the equation:
$14x + 5=17x-1$
Subtract $14x$ from both sides:
$5 = 3x-1$
Add 1 to both sides:
$6 = 3x$
Divide both sides by 3:
$x = 2$
Find $m\angle FLG$:
$m\angle FLG=14x + 5=14\times2+5=28 + 5=33^{\circ}$
Since $m\angle FLH=2m\angle FLG$ (because of angle - bisector), then $m\angle FLH=2\times33^{\circ}=66^{\circ}$

Answer:

1. Another name for $\angle CAD$ is $\angle DAC$.
2. $m\angle FLH = 66^{\circ}$