Question

directions: if l || m, solve for x and y.

1. (9x + 25)° (13x - 19)° (17y + 5)°
2. (3x - 29)° (8y + 17)° (6x - 7)°
3. 49° (3x)° (7x - 23)° (11y - 1)°
4. (7y - 20)° (5x - 38)° (3x - 4)° © gina wilson (all things alg)

Explanation:

1. For problem 10:

• Since \(l\parallel m\), the corresponding - angles are equal. So, \(3x - 29=6x - 7\).

Step1: Rearrange the equation

Subtract \(3x\) from both sides of the equation \(3x - 29 = 6x - 7\). We get \(-29=3x - 7\).

Step2: Isolate the variable \(x\)

Add 7 to both sides of the equation \(-29 = 3x - 7\). Then \(-29 + 7=3x\), which simplifies to \(-22 = 3x\). So, \(x=-\frac{22}{3}\).

• Also, since the angles \((8y + 17)^{\circ}\) and \((6x - 7)^{\circ}\) are corresponding - angles (or we can use the fact that they are related by the parallel - line properties), but we first need to find \(y\) using another relationship. Let's assume we use the fact that the sum of angles on a straight - line or some other angle - relationship. However, if we consider the parallel - line properties, we know that the angles are equal. But we made a mistake above. The correct equation for parallel lines is \(3x-29 + 6x - 7=180\) (since they are same - side interior angles).

Step1: Combine like terms

\((3x+6x)+(-29 - 7)=180\), which gives \(9x-36 = 180\).

Step2: Add 36 to both sides

\(9x=180 + 36\), so \(9x=216\).

Step3: Solve for \(x\)

Divide both sides by 9: \(x = 24\).

• Now, since the angles \((8y + 17)^{\circ}\) and \((6x - 7)^{\circ}\) are corresponding angles, \(8y+17=6x - 7\). Substitute \(x = 24\) into the equation:

Step1: Substitute \(x\) value

\(8y+17=6\times24 - 7\).
\(8y+17=144 - 7\).
\(8y+17=137\).

Step2: Subtract 17 from both sides

\(8y=137 - 17\), so \(8y = 120\).

Step3: Solve for \(y\)

Divide both sides by 8: \(y = 15\).

Answer:

\(x = 24,y = 15\)

1. For problem 11:

• Since \(l\parallel m\), the vertical angles and the angle - relationships due to parallel lines are used. The angles \((3x)^{\circ}\) and \((7x - 23)^{\circ}\) are vertical angles, so \(3x=7x - 23\).

Step1: Rearrange the equation

Subtract \(3x\) from both sides: \(0 = 4x-23\).

Step2: Isolate the variable \(x\)

Add 23 to both sides: \(4x=23\), so \(x=\frac{23}{4}=5.75\).

• Also, the angles \((3x)^{\circ}\) and \((11y - 1)^{\circ}\) are corresponding angles. Substitute \(x = 5.75\) into the equation \(3x=11y - 1\).

Step1: Substitute \(x\) value

\(3\times5.75=11y - 1\).
\(17.25=11y - 1\).

Step2: Add 1 to both sides

\(17.25 + 1=11y\), so \(18.25=11y\).

Step3: Solve for \(y\)

\(y=\frac{18.25}{11}=\frac{73}{44}\approx1.66\).