Question

name nora hidalgo
unit 2 | lesson 1-3 review
period
(diagrams: d: (14x + 2) and (13x + 9); e: (3x - 33) and (2x + 26); f: (3x + 10) and (5x + 90); g: (x + 15) and (3x + 5))

Explanation:

To solve for \( x \) in each diagram (D, E, F, G), we use properties of parallel lines and transversals (e.g., corresponding angles, alternate interior angles, consecutive interior angles, or vertical angles). Here, we assume the angles given are either equal (corresponding/alternate) or supplementary (consecutive interior). Let's solve each:

Diagram D:

Angles: \( 13x + 9 \) and \( 14x + 2 \)
Assume they are equal (corresponding/alternate angles):

Step 1: Set angles equal

\( 13x + 9 = 14x + 2 \)

Step 2: Solve for \( x \)

Subtract \( 13x \) from both sides: \( 9 = x + 2 \)
Subtract 2: \( x = 7 \)

Diagram E:

Angles: \( 3x - 33 \) and \( 2x + 26 \)
Assume they are equal (corresponding/alternate angles):

Step 1: Set angles equal

\( 3x - 33 = 2x + 26 \)

Step 2: Solve for \( x \)

Subtract \( 2x \): \( x - 33 = 26 \)
Add 33: \( x = 59 \)

Diagram F:

Angles: \( 3x + 10 \) and \( 5x + 90 \)
Assume they are supplementary (consecutive interior angles, sum to \( 180^\circ \)):

Step 1: Set sum to \( 180^\circ \)

\( (3x + 10) + (5x + 90) = 180 \)

Step 2: Simplify and solve

Combine like terms: \( 8x + 100 = 180 \)
Subtract 100: \( 8x = 80 \)
Divide by 8: \( x = 10 \)

Diagram G:

Angles: \( x + 15 \) and \( 3x + 5 \)
Assume they are equal (corresponding/alternate angles):

Step 1: Set angles equal

\( x + 15 = 3x + 5 \)

Step 2: Solve for \( x \)

Subtract \( x \): \( 15 = 2x + 5 \)
Subtract 5: \( 10 = 2x \)
Divide by 2: \( x = 5 \)

Final Answers:

• Diagram D: \( \boldsymbol{x = 7} \)
• Diagram E: \( \boldsymbol{x = 59} \)
• Diagram F: \( \boldsymbol{x = 10} \)
• Diagram G: \( \boldsymbol{x = 5} \)

Answer:

To solve for \( x \) in each diagram (D, E, F, G), we use properties of parallel lines and transversals (e.g., corresponding angles, alternate interior angles, consecutive interior angles, or vertical angles). Here, we assume the angles given are either equal (corresponding/alternate) or supplementary (consecutive interior). Let's solve each:

Diagram D:

Angles: \( 13x + 9 \) and \( 14x + 2 \)
Assume they are equal (corresponding/alternate angles):

Step 1: Set angles equal

\( 13x + 9 = 14x + 2 \)

Step 2: Solve for \( x \)

Subtract \( 13x \) from both sides: \( 9 = x + 2 \)
Subtract 2: \( x = 7 \)

Diagram E:

Angles: \( 3x - 33 \) and \( 2x + 26 \)
Assume they are equal (corresponding/alternate angles):

Step 1: Set angles equal

\( 3x - 33 = 2x + 26 \)

Step 2: Solve for \( x \)

Subtract \( 2x \): \( x - 33 = 26 \)
Add 33: \( x = 59 \)

Diagram F:

Angles: \( 3x + 10 \) and \( 5x + 90 \)
Assume they are supplementary (consecutive interior angles, sum to \( 180^\circ \)):

Step 1: Set sum to \( 180^\circ \)

\( (3x + 10) + (5x + 90) = 180 \)

Step 2: Simplify and solve

Combine like terms: \( 8x + 100 = 180 \)
Subtract 100: \( 8x = 80 \)
Divide by 8: \( x = 10 \)

Diagram G:

Angles: \( x + 15 \) and \( 3x + 5 \)
Assume they are equal (corresponding/alternate angles):

Step 1: Set angles equal

\( x + 15 = 3x + 5 \)

Step 2: Solve for \( x \)

Subtract \( x \): \( 15 = 2x + 5 \)
Subtract 5: \( 10 = 2x \)
Divide by 2: \( x = 5 \)

Final Answers:

• Diagram D: \( \boldsymbol{x = 7} \)
• Diagram E: \( \boldsymbol{x = 59} \)
• Diagram F: \( \boldsymbol{x = 10} \)
• Diagram G: \( \boldsymbol{x = 5} \)