Question

for questions 13 - 15, find the values of x and y if l || m.
13.
14.
15.

Explanation:

Question 13

Step1: Use the property of alternate - interior angles

Since \(l\parallel m\), \(10x - 17=8x + 1\) (alternate - interior angles are equal).

$$
LATEXBLOCK0
$$

Step2: Use the property of supplementary angles

\((6y + 29)+(8x + 1)=180\) (consecutive - interior angles are supplementary). Substitute \(x = 9\) into the equation:

$$
LATEXBLOCK1
$$

Step1: Use the property of alternate - interior angles

Since \(l\parallel m\), \(7x-30 = 5x + 14\) (alternate - interior angles are equal).

$$
LATEXBLOCK0
$$

Step2: Use the property of corresponding angles

\(3y + 11=7x-30\) (corresponding angles are equal). Substitute \(x = 22\) into the equation:

$$
LATEXBLOCK1
$$

Step1: Use the property of alternate - interior angles

Since \(l\parallel m\), \(23x-16=8x - 21\) (alternate - interior angles are equal).

$$
LATEXBLOCK0
$$

Step2: Use the property of supplementary angles

\((7y-23)+(8x - 21)=180\) (consecutive - interior angles are supplementary). Substitute \(x=-\frac{1}{3}\) into the equation:

$$
LATEXBLOCK1
$$

Answer:

\(x = 9,y = 13\)

Question 14