α = 85^(∘)
θ = 68^(∘) Relationships: See solution.
Practice makes perfect
To find the measure of α, we will highlight certain parts of the diagram.
The ray is a transversal to the two lines. Since α and 85^(∘) have corresponding positions with respect to the transversal, they are corresponding angles. Due to the fact that the lines are parallel, we can use the Corresponding Angles Theorem and claim that the angles are congruent.
To determine θ, we will highlight the second ray and mark the corresponding angle to 112^(∘).
The corresponding angle we just marked, forms a Linear Pair with θ. By the Linear Pair Postulate, we know that they sum to 180^(∘). With this we can write an equation.
112^(∘)+θ=180^(∘)
Let's solve the equation for θ.
