Question

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

Answer 1

To determine which equation to use, we first need to understand the angle relationships at the intersection of lines m and n.

1. If the angle represented by \(5y + 10\) is supplementary to another angle (e.g., 85 degrees), we would use the equation:

\[
(5y + 10) + 85 = 180
\]

This is because supplementary angles add up to 180 degrees.

So, the correct choice for Part 1 is:

**(5y + 10) + 85 = 180**

For Part 2, we will use this equation to solve for \(y\):

\[
(5y + 10) + 85 = 180
\]

First, we simplify the left side:

\[
5y + 10 + 85 = 180
\]
\[
5y + 95 = 180
\]

Next, subtract 95 from both sides:

\[
5y = 180 - 95
\]
\[
5y = 85
\]

Now, divide by 5:

\[
y = \frac{85}{5} = 17
\]

Now we can find the measure of the angle:

\[
5y + 10 = 5(17) + 10 = 85 + 10 = 95 \text{ degrees}
\]

So, for Part 2:

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

The final answers are:

**y = 17**

**5y + 10 = 95 degrees**