Consider a pair of parallel lines cut by a transversal that creates two angles

Question

∠
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 \( \boxed{15} \).