Try to find the described angles on the given figure.
A
x=64^(∘)
B
They are equal to each other.
Practice makes perfect
We want to find the value of x. Let's take a look at the given figure.
First we will find the value of m. We will use the fact that the two angles that measure m^(∘) and the angle that measures 64^(∘) are supplementary angles. This means that their measures add up to 180^(∘).
m^(∘)+ 64^(∘)+ m^(∘)=180^(∘)Now we can solve for m.
Next, notice that upper and lower edges of the table are parallel to each other. The distance that the puck travels from the lower to the upper edge is a transversal.
We know that alternate interior angles are congruent if the transversal intersects parallel lines. Because of this, the sum of the angles that measure x^(∘) and 58^(∘) is equal to the sum of the angles that measure 64^(∘) and 58^(∘).
With this, we can write the following equation.
58^(∘)+ x^(∘)= 64^(∘)+ 58^(∘)
Let's solve it for x.
We want to find the relationship between two angles. One angle is the angle that the puck hits the edge of the table, let's call it a. The other is the angle the puck leaves the edge of the table, we can call it b.
Now let's look at our diagram. We will focus on the point where the puck hits the edge for the second time.
We can see that the measure of the angle that the puck hits the edge of the table is equal to the measure of the angle it leaves the edge of the table. This is true for any time the puck hits the edge of the table.
