Before you can find y^(∘) you have to find x^(∘).
x^(∘)=26^(∘)
y^(∘)=64^(∘)
Practice makes perfect
According to the Corollary to the Triangle Sum Theorem, the acute angles of a right triangle are complementary. Therefore, we can write the equation
x^(∘)+64^(∘)=90^(∘)
Let's solve this equation.
When we know the measure of x^(∘), we can use this information to find the alternate interior angle which we have highlighted and labeled as z in the figure below.
According to the Alternate Interior Angles Theorem, if two parallel lines are cut by a transversal, then the pair of alternate interior angles are congruent. Therefore, we can say that
z^(∘)=26^(∘).
To find the measure of y^(∘), we can use the Corollary to the Triangle Sum Theorem which states that the acute angles of a right triangle are complementary. Therefore, we can write the following equation
y^(∘)+26^(∘) = 90^(∘).
Let's solve this equation.
