We are given a diagram with two parallel lines,
r and
t, cut by a transversal. The angles formed are labeled:
- One angle:
(5y – 9)°
- Another angle:
(5x + 4)°
- A third angle:
3x°
And we’re told:
r ∥ t
---
Step 1: Identify the relationship between the angles
Looking at the diagram (even though not to scale), the angle labeled
(5x + 4)° and the angle labeled
3x° appear to be
same-side interior angles — they are on the same side of the transversal and between the two parallel lines.
>
Key fact: When two parallel lines are cut by a transversal,
same-side interior angles are supplementary — that is, they add up to
180°.
So:
>
(5x + 4) + 3x = 180
Let’s solve for
x:
```
5x + 4 + 3x = 180
8x + 4 = 180
8x = 176
x = 22
```
✔ So,
x = 22
---
Step 2: Find y
Now look at the angle labeled
(5y – 9)°. It appears to be
corresponding to the angle labeled
3x°, because they are in matching positions relative to the transversal and the parallel lines.
>
Key fact: Corresponding angles are
equal when lines are parallel.
So:
>
5y – 9 = 3x
We already found
x = 22, so plug that in:
```
5y - 9 = 3(22)
5y - 9 = 66
5y = 75
y = 15
```
✔ So,
y = 15
---
Step 3: Find x + y
```
x + y = 22 + 15 = 37
```
---
✔ Final Answer: A) 37
---
Summary:
- Used
same-side interior angles are supplementary to find
x = 22
- Used
corresponding angles are equal to find
y = 15
- Added them:
x + y = 37
Answer:
A) 37
Parent Tip: Review the logic above to help your child master the concept of sat math practice worksheet.
