We are given two parallel lines,
a and
b, cut by a transversal line
t.
There are two angles marked:
- One angle is
60°, between line
a and transversal
t.
- Another angle is
8x - 4, between line
b and transversal
t.
Looking at their positions:
The 60° angle and the (8x - 4)° angle are on the
same side of the transversal and both are
between the two parallel lines. That makes them
consecutive interior angles (also called same-side interior angles).
When two parallel lines are cut by a transversal,
consecutive interior angles are supplementary — meaning they add up to
180°.
So we can write the equation:
> 60 + (8x - 4) = 180
Now solve step by step:
Step 1: Combine like terms on the left:
> 60 - 4 + 8x = 180
> 56 + 8x = 180
Step 2: Subtract 56 from both sides:
> 8x = 180 - 56
> 8x = 124
Step 3: Divide both sides by 8:
> x = 124 ÷ 8
> x = 15.5
Let’s check:
Plug x = 15.5 into 8x - 4:
> 8*(15.5) - 4 = 124 - 4 = 120
Then 60 + 120 = 180 → Correct!
Final Answer:
15.5
Parent Tip: Review the logic above to help your child master the concept of parallel lines cut by transversal worksheet.
