a What type of angle relationship is held by ∠ r and ∠ k?
B
b What type of angle relationship is held by ∠ t and ∠ q? How about ∠ c and ∠ t?
C
c What type of angle relationship is held by ∠ g and ∠ q?
A
a x=6^(∘)
Justification: See solution.
B
b m∠ q = 66^(∘)
Justification: See solution.
C
c m∠ q = 92^(∘)
Justification: See solution.
Practice makes perfect
a Let's highlight some important parts of the diagram. Note that that ∠ r and ∠ k are alternate interior angles.
Since the two lines cut by the transversal are parallel, we can claim that they are congruent by the Alternate Interior Angles Theorem. Let's add this information to the diagram and substitute ∠ r and ∠ k with their respective expression.
Because the two pairs of lines are parallel, we know that ∠ t and ∠ c are supplementary angles and ∠ t and ∠ q are corresponding. Recall that corresponding angles are congruent when dealing with parallel lines cut by a transversal.
Since ∠ t and ∠ q are congruent, we know that ∠ c and ∠ q must be supplementary angles as well. With this, we can write an equation.
m∠ c+m∠ q = 180^(∘)
Since we know m∠ c, we can solve for m∠ q.
