Question

Consider a pair of parallel lines cut by a transversal that creates two angles
∠
X
∠X and
∠
Y
∠Y, where
∠
X
∠X and
∠
Y
∠Y are corresponding angles.

​
∠
X
=
5
x
+
3
0
∘
∠X=5x+30
∘


​
∠
Y
=
3
x
+
6
0
∘
∠Y=3x+60
∘


​The value of
x
x is
degree.

Answer 1

Since angles ∠X and ∠Y are corresponding angles created by the transversal cutting parallel lines, they are equal:

\[
∠X = ∠Y
\]

We can set up the equation:

\[
5x + 30 = 3x + 60
\]

Now, we will solve for \( x \):

1. Subtract \( 3x \) from both sides:

\[
5x - 3x + 30 = 60
\]
\[
2x + 30 = 60
\]

2. Subtract 30 from both sides:

\[
2x = 60 - 30
\]
\[
2x = 30
\]

3. Divide both sides by 2:

\[
x = \frac{30}{2}
\]
\[
x = 15
\]

Thus, the value of \( x \) is \( \boxed{15} \).