Question

1. $mangle hgf = 16x + 4$, $mangle egf=110^{circ}$, and $mangle hge = 3x + 11$. find $x$.
2. $mangle vut = 175^{circ}$, $mangle vuj = 17x - 3$, and $mangle jut = 17x + 8$. find $x$.
3. $mangle fcd=x + 41$, $mangle bcf=x + 78$, and $mangle bcd = 95^{circ}$. find $x$.
4. find $x$ if $mangle bjk = 146+2x$, $mangle ijk = 172^{circ}$, and $mangle ijb = 2x + 26$.

Explanation:

11)

Step1: Use angle - addition postulate

$m\angle HGF=m\angle HGE + m\angle EGF$
$16x + 4=(3x + 11)+110$

Step2: Simplify the equation

$16x+4 = 3x+121$
$16x-3x=121 - 4$
$13x=117$

Step3: Solve for x

$x = 9$

Step1: Use angle - addition postulate

$m\angle VUT=m\angle VUJ+m\angle JUT$
$175=(17x - 3)+(17x + 8)$

Step2: Simplify the equation

$175=34x+5$
$34x=175 - 5$
$34x=170$

Step3: Solve for x

$x = 5$

Step1: Use angle - addition postulate

$m\angle BCD=m\angle BCF+m\angle FCD$
$95=(x + 78)+(x + 41)$

Step2: Simplify the equation

$95=2x+119$
$2x=95 - 119$
$2x=-24$

Step3: Solve for x

$x=-12$

Answer:

$x = 9$

12)