Question

**#3.) what is the value of x and y?
a.) x = 13,y = 48
b.) x = -3.04,y = 132
c.) x = 13,y = 132
d.) x = -3.04,y = 48
#4.) in the diagram below $overleftrightarrow{ab}paralleloverleftrightarrow{cd}$. if $mangle hgd=(5x + 20)^{circ}$ and $mangle efb=(x + 40)^{circ}$ determine the number of degrees in all 8 angles and label them in the diagram below.
#5.) in the diagram below of $\triangle abc$, $mangle a=(x + 45)^{circ}$, $mangle b=(x - 15)^{circ}$, and $mangle c=(2x - 30)^{circ}$. determine $mangle a$.
#6.) unit 0 spiral: which the following could represent the equation of a line perpendicular to $2y+3x = 8$?
a. $y=\frac{2}{3}x + 1$
b. $y=\frac{3}{2}x - 5$
c. $y=-\frac{2}{3}x + 4$
d. $y=-\frac{3}{2}x + 7$

Explanation:

#3

Step1: Set up equation using vertical - angle property

Vertical angles are equal. So, $5x−17 = 48$.
$5x=48 + 17$
$5x=65$
$x = 13$

Step2: Find the value of $y$

The angle $y$ and the angle $(5x - 17)^{\circ}$ are supplementary (linear - pair of angles), so $y+48=180$.
$y=180 - 48$
$y = 132$

Step1: Use the property of corresponding angles

Since $\overline{AB}\parallel\overline{CD}$, $\angle HGD$ and $\angle EFB$ are corresponding angles, so $5x + 20=x + 40$.
$5x-x=40 - 20$
$4x=20$
$x = 5$

Step2: Find the measure of angles

$\angle HGD=5x + 20=5\times5+20=45^{\circ}$
$\angle EFB=x + 40=5 + 40=45^{\circ}$
Corresponding angles are equal, alternate - interior angles are equal, and vertical angles are equal. So, all the eight angles:
$\angle HGD=\angle EFB=\angle AFE=\angle CGH = 45^{\circ}$
$\angle HGA=\angle BFG=\angle DGF=\angle EFC=180 - 45=135^{\circ}$

#5

Step1: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. So, $(x + 45)+(x - 15)+(2x-30)=180$.
$x + 45+x - 15+2x-30=180$
$4x=180$
$x = 45$

Step2: Find $m\angle A$

$m\angle A=x + 45=45+45=90^{\circ}$

Answer:

c. $x = 13,y = 132$

#4