Let's begin with finding the value of x. Then we will use it to calculate the value of y.
Value of x
In order to find the value of x, we need to analyze the given diagram. What is the relationship between the angles measuring (x+36)^(∘) and 78^(∘)?
These are consecutive interior angles. The Consecutive Interior Angles Theorem tells us that consecutive interior angles formed by parallel lines and a transversal are supplementary.
Therefore, these angles are supplementary and the sum of their measures is 180^(∘).
78+(x+36)=180
We can solve this equation to find the value of x.
To find the value of y, we need to find the relationship between the angles which measure (2y)^(∘) and 110^(∘). Let's analyze the diagram once more.
Notice that they are also consecutive interior angles.
2y+110=180
To find the value of y, let's solve this equation!
