Question

identify x then find the missing angle measurements
(13x - 21)°
(5x + 75)°
(11x - 47)°
(6x - 2)°

Explanation:

Step1: Set up the equation for the first pair

Set \(13x-21 = 5x + 75\) based on angle - equality.

Step2: Simplify the equation

Subtract \(5x\) from both sides: \(8x-21 = 75\).

Step3: Isolate the variable term

Add 21 to both sides: \(8x=96\).

Step4: Solve for \(x\)

Divide by 8: \(x = 12\).

Step5: Find the angle measures

Substitute \(x = 12\) into the angle expressions.

Step6: Set up the equation for the second pair

Set \(11x-47=6x - 2\) based on angle - equality.

Step7: Simplify the equation

Subtract \(6x\) from both sides: \(5x-47=-2\).

Step8: Isolate the variable term

Add 47 to both sides: \(5x = 45\).

Step9: Solve for \(x\)

Divide by 5: \(x = 9\).

Step10: Find the angle measures

Substitute \(x = 9\) into the angle expressions.

Answer:

For the first pair of angles:

1. First, find \(x\):

• Given that \((13x - 21)^{\circ}\) and \((5x + 75)^{\circ}\) are equal (assuming they are corresponding or alternate - interior angles for parallel lines \(l\) and \(m\)).
• Set up the equation \(13x-21 = 5x + 75\).
• Subtract \(5x\) from both sides: \(13x-5x-21=5x - 5x+75\), which simplifies to \(8x-21 = 75\).
• Add 21 to both sides: \(8x-21 + 21=75 + 21\), so \(8x=96\).
• Divide both sides by 8: \(x=\frac{96}{8}=12\).
• Then find the angle measures:
• Substitute \(x = 12\) into \((13x - 21)\): \(13\times12-21=156 - 21=135^{\circ}\).
• Substitute \(x = 12\) into \((5x + 75)\): \(5\times12+75=60 + 75=135^{\circ}\).

For the second pair of angles:

1. First, find \(x\):

• Given that \((11x - 47)^{\circ}\) and \((6x - 2)^{\circ}\) are equal (assuming they are corresponding or alternate - interior angles for parallel lines \(l\) and \(m\)).
• Set up the equation \(11x-47=6x - 2\).
• Subtract \(6x\) from both sides: \(11x-6x-47=6x - 6x-2\), which simplifies to \(5x-47=-2\).
• Add 47 to both sides: \(5x-47 + 47=-2 + 47\), so \(5x = 45\).
• Divide both sides by 5: \(x=\frac{45}{5}=9\).
• Then find the angle measures:
• Substitute \(x = 9\) into \((11x - 47)\): \(11\times9-47=99 - 47=52^{\circ}\).
• Substitute \(x = 9\) into \((6x - 2)\): \(6\times9-2=54 - 2=52^{\circ}\).