Two adjacent angles, angle 1 and angle 2, form a resulting angle with a measure of 135°

Question

.

Part 1: If the measure of angle 1 = (2x)°
and the measure of angle 2 is (2x+7)°
, which equation may be used to determine the value of x?

(1 point)
Responses

2x+(2x+7)=180
2 x plus open paren 2 x plus 7 close paren is equal to 180

2x+(2x+7)=135
2 x plus open paren 2 x plus 7 close paren is equal to 135

2x=2x+7
2 x is equal to 2 x plus 7

2x−(2x+7)=135
2 x minus open paren 2 x plus 7 close paren is equal to 135
Question 2
(3 points)
Part 2: Complete the following statements after solving the equation in Part 1.

x =

Angle 2x has a measure of
degrees.

Angle 2x + 7 has a measure of
degrees.

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Answer 1

Part 1:

Given that the measures of angle 1 and angle 2 combine to form a resulting angle of 135°, the correct equation to represent the problem would be:

2x + (2x + 7) = 135

This is because angle 1 is \(2x\) and angle 2 is \(2x + 7\), and together they equal 135°.

Part 2:

To solve for \(x\):

1. Combine the terms in the equation: \[ 2x + (2x + 7) = 135 \] simplifies to \[ 4x + 7 = 135 \]

2. Subtract 7 from both sides: \[ 4x = 135 - 7 \] \[ 4x = 128 \]

3. Divide both sides by 4: \[ x = \frac{128}{4} = 32 \]

Now, we can find the measures of the angles:

• Angle 1 (2x): \[ 2x = 2(32) = 64 \text{ degrees} \]

• Angle 2 (2x + 7): \[ 2x + 7 = 64 + 7 = 71 \text{ degrees} \]

Summary of Answers for Part 2:

• \(x = 32\)
• Angle \(2x\) has a measure of 64 degrees.
• Angle \(2x + 7\) has a measure of 71 degrees.