Question

directions: if ( lparallel m ), solve for ( x ) and ( y ).
9.
(9x + 25)°
(13x - 19)° (17y + 5)°
10.
(3x - 29)° (8y + 17)°
(6x - 7)°
11.
49°
(3x)° (11y - 1)°
(7x - 23)°
12.
(7y - 20)° (5x - 38)°
(3x - 4)°
© gina wilson (all things algebra®, llc). 2014 - 20

Explanation:

Step1: Identify angle - relationship for question 9

Since \(l\parallel m\), the angles \((9x + 25)^{\circ}\) and \((13x-19)^{\circ}\) are alternate - exterior angles, so \(9x + 25=13x-19\).

$$
LATEXBLOCK0
$$

The angles \((13x - 19)^{\circ}\) and \((17y + 5)^{\circ}\) are corresponding angles, so \(13x-19=17y + 5\). Substitute \(x = 11\) into the equation:

$$
LATEXBLOCK1
$$

Step2: Identify angle - relationship for question 10

The angles \((3x - 29)^{\circ}\) and \((6x - 7)^{\circ}\) are same - side interior angles, so \((3x - 29)+(6x - 7)=180\).

$$
LATEXBLOCK2
$$

The angles \((3x - 29)^{\circ}\) and \((8y + 17)^{\circ}\) are corresponding angles, so \(3x-29=8y + 17\). Substitute \(x = 24\) into the equation:

$$
LATEXBLOCK3
$$

Step3: Identify angle - relationship for question 11

The angles \((3x)^{\circ}\) and \(49^{\circ}\) are vertical angles, so \(3x=49\), \(x=\frac{49}{3}\approx16.33\).
The angles \((7x - 23)^{\circ}\) and \((11y - 1)^{\circ}\) are corresponding angles. Substitute \(x=\frac{49}{3}\) into \(7x-23\):

$$
LATEXBLOCK4
$$

Step4: Identify angle - relationship for question 12

The angles \((5x - 38)^{\circ}\) and \((3x - 4)^{\circ}\) are same - side interior angles, so \((5x - 38)+(3x - 4)=180\).

$$
LATEXBLOCK5
$$

The angles \((7y - 20)^{\circ}\) and \((3x - 4)^{\circ}\) are corresponding angles. Substitute \(x = 27.75\) into \(3x-4\):

$$
LATEXBLOCK6
$$

Answer:

Question 9: \(x = 11,y = 7\)
Question 10: \(x = 24,y = 3.25\)
Question 11: \(x=\frac{49}{3},y=\frac{277}{33}\)
Question 12: \(x=\frac{111}{4},y = 14.18\)