The diagram shows line m intersecting line n and shows some of the angle measures.

Part 1: Which equation should be used to determine the value of y?

(1 point)
Responses

5y+10=85
5 y plus 10 is equal to 85

(5y+10)+85=90
open paren 5 y plus 10 close paren plus 85 is equal to 90

(5y+10)−85=180
open paren 5 y plus 10 close paren minus 85 is equal to 180

(5y+10)+85=180
open paren 5 y plus 10 close paren plus 85 is equal to 180
Question 2
Part 2: Using the equation you chose, determine the value of y and measure of the angles.(2 points)
y=


5y+10=

degrees

1 answer

To answer your question, we need to examine the properties of angles formed when two lines intersect. The angles around the point of intersection provide relationships that can help us formulate the right equation.

  1. Identifying the relationship: If one angle measures \( 85^\circ \) and another angle is expressed as \( 5y + 10 \), we can assume that they are either supplementary (adding up to \( 180^\circ \)) or they might be vertical angles (equal). Based on the equations you provided, it seems likely that \( 5y + 10 \) and \( 85^\circ \) are supplementary.

  2. Choosing the right equation: The correct equation to use, assuming \( 5y + 10 \) and \( 85^\circ \) are supplementary, would be: \[ (5y + 10) + 85 = 180 \]

So, the response to Part 1 would be:

  • (5y + 10) + 85 = 180

For Part 2

Now, we will solve for \( y \) using the equation (5y + 10) + 85 = 180:

\[ 5y + 10 + 85 = 180 \] \[ 5y + 95 = 180 \] \[ 5y = 180 - 95 \] \[ 5y = 85 \] \[ y = \frac{85}{5} = 17 \]

Now, substitute back to find the angle measure: \[ 5y + 10 = 5(17) + 10 = 85 + 10 = 95 \]

Thus, the values are:

  • \( y = 17 \)
  • \( 5y + 10 = 95 \) degrees

Final Answers:

  • Part 1 (Equation): (5y + 10) + 85 = 180
  • Part 2: \( y = 17 \), \( 5y + 10 = 95 \) degrees