Part 1: Which two equations can be used to determine the measure of these two angles?

(2 points)
Responses

4x−(7x−9)=90
4 x minus open paren 7 x minus 9 close paren is equal to 90

4x+(7x−9)=180
4 x plus open paren 7 x minus 9 close paren is equal to 180

(4x+(7x−9)=90

11x−9=90
11 x minus 9 is equal to 90

3x−9=90
3 x minus 9 is equal to 90

11x−9=180
11 x minus 9 is equal to 180
Question 2
Part 2: Use the image above to complete the following:(3 points)
x=


Angle 4x =
degrees

Angle 7x - 9 =
degrees

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1 answer

To determine the measure of the two angles, you typically need to use the relationships between them. Assuming these angles are part of a geometric configuration (like adjacent angles, supplementary angles, etc.), the appropriate equations can vary based on those relationships.

From your listed options, it seems likely that either of these pairs could represent the functional relationship between the angles:

  1. 4x + (7x - 9) = 180: This suggests that the two angles are supplementary, meaning their measures add up to 180 degrees.
  2. 11x - 9 = 90: This suggests that the sum of the angles is equal to 90 degrees, indicating that they are complementary.

If we assume the first option is correct and they are supplementary, you would then solve for \( x \):

  1. Start with the equation: \[ 4x + (7x - 9) = 180 \] Simplifying gives: \[ 4x + 7x - 9 = 180 \] \[ 11x - 9 = 180 \] Adding 9 to both sides: \[ 11x = 189 \] Dividing by 11 gives: \[ x = \frac{189}{11} \approx 17.18 \]

Now, to find the measures of the angles:

  • For Angle \( 4x \): \[ 4x = 4 \times \frac{189}{11} \approx \frac{756}{11} \approx 68.73 \text{ degrees} \]

  • For Angle \( 7x - 9 \): \[ 7x - 9 = 7 \times \frac{189}{11} - 9 \approx \frac{1323}{11} - 9 = \frac{1323 - 99}{11} = \frac{1224}{11} \approx 111.27 \text{ degrees} \]

Therefore, you have:

  • \( x \approx 17.18 \)
  • Angle \( 4x \approx 68.73 \) degrees
  • Angle \( 7x - 9 \approx 111.27 \) degrees

Make sure to adjust according to your specific context regarding angle relationships!