Two parallel lines are crossed by a transversal.

Question

Vertical and parallel lines h and i are cut by transversal g. At the intersection of lines h and g, the uppercase right angle is 70 degrees and the bottom left angle is x degrees.
What is the value of x?

x = 40
x = 70
x = 110
x = 130

Answer 1

When two parallel lines are crossed by a transversal, several angle relationships are established.

In this scenario, we have two parallel lines (h and i) and a transversal (g). At the intersection of lines h and g, there is a right angle which is 70 degrees.

Since we have a right angle formed, the angles on a straight line add up to 180 degrees. Given that one angle is 70 degrees, we can find the measure of angle \( x \) (which is the bottom left angle at the intersection of line h and line g) as follows:

\[ x + 70 = 180 \]

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

\[ x = 180 - 70 \] \[ x = 110 \]

Thus, the value of \( x \) is \( 110 \).

So the correct answer is \( x = 110 \).