The angles of a linear pair are supplementary. Therefore, we can calculate c by adding the measures of the angles in the linear pair and equating the sum with 180^(∘).
m∠c+123^(∘)= 180^(∘) ⇔ m∠c = 57^(∘)
b From the diagram, we can identify a few angle relationships.
By the Vertical Angles Theorem, we know that vertical angles are congruent. Also, since the two lines cut by the transversal are parallel, we can claim by the Alternate Interior Angles Theorem that these are congruent as well. However, to find the measure of these angles, we first have to find the value of m∠f. As in Part A, we will set the sum of the angles in the linear pair equal to 180^(∘).
m∠f+82^(∘)=180^(∘) ⇔ m∠f= 98^(∘)
Having calculated the measure of ∠f, we also know the measures of ∠d and ∠e as they are congruent to ∠f.
c From the diagram, we can identify a few angle relationships.
By the Vertical Angles Theorem, we know that vertical angles are congruent. Also, since the two lines cut by the transversal are parallel, we can claim by the Alternate Interior Angles Theorem that these are congruent as well. Therefore, all of the unknown angles have a measure of 75^(∘).
