We want to find the value of a. First we will label the parallel lines as k and l, and their transversal as t. Let's take a look at the given picture using these assigned labels.
When we have parallel lines cut by a transversal, several types of angles pairs are formed. Let's recall the definition of one of them — alternate interior angles.
Alternate Interior Angles
They lie between the two lines on opposite sides of the transversal.
We know that alternate interior angles are congruent if the transversal intersects parallel lines. Because of this, the measure of the angle adjacent to the angle a^(∘) is 70^(∘). Let's add this information to the diagram.
Next, notice that the bridge is a level surface. This means that the line created by the bridge and the line l are perpendicular — together they form a right angle. We know that the measure of a right angle is 90^(∘).
Now we will use fact that the measures of angle a^(∘) and the angle adjacent to it, the 70^(∘) angle, need to add up to 90^(∘).
a^(∘)+ 70^(∘)= 90^(∘) ⇕ a^(∘)=20^(∘)
The value of a is 20^(∘).
