Question

complete the sentences to describe angle qhj. angles pqr and qhj are ⓐ congruent ⓑ supplementary ⓒ complementary because they are ⓐ consecutive ⓑ corresponding ⓒ alternate exterior angles. the measure of angle qhj is \boxed{}°.

Explanation:

To solve this, we analyze the angle relationships (though the diagram isn't fully shown, we assume typical parallel line - transversal setups):

Step 1: Determine the relationship type (first blank)

• Congruent angles have equal measures. Supplementary angles sum to \(180^\circ\), and complementary sum to \(90^\circ\).
• If \(PQ\) and \(HJ\) are parallel (implied by the angle - naming and relationship context) and \(QR\) and \(HJ\) related via a transversal, corresponding angles (second blank analysis) are congruent. So the first blank is "A. congruent".

Step 2: Determine the angle - pair type (second blank)

• Consecutive angles are adjacent or on the same side of a transversal. Corresponding angles are in the same relative position at each intersection of a transversal with parallel lines. Alternate exterior are on opposite sides, outside the parallel lines.
• For angles \(PQR\) and \(QHJ\) (assuming a transversal cutting parallel lines), they are in the same relative position, so they are "A. corresponding" angles.

Step 3: Find the measure of \(\angle QHJ\)

• If \(\angle PQR\) (not shown, but if we assume a typical problem, say \(\angle PQR = 60^\circ\) or another value, but since corresponding angles are congruent, if \(\angle PQR\) has a measure (e.g., if \(\angle PQR = 60^\circ\)), then \(\angle QHJ=\angle PQR\). But since the problem likely has \(\angle PQR\) with a measure (maybe from a diagram not fully provided, but in standard problems, if they are corresponding and congruent, and if \(\angle PQR\) is, say, \(60^\circ\), then \(\angle QHJ = 60^\circ\) (this depends on the diagram, but the key is that congruent corresponding angles have equal measures).

Final Answers for the blanks:

• First blank: A. congruent
• Second blank: A. corresponding
• For the measure, if we assume \(\angle PQR\) (from typical problems, say if \(\angle PQR = 60^\circ\)) then \(\angle QHJ=\boldsymbol{60}\) (the actual value depends on the diagram, but the process is using corresponding - congruent angle relationship).

If we assume the diagram has \(\angle PQR = 60^\circ\) (a common example), then:

Step1: Identify angle relationship

Angles \(PQR\) and \(QHJ\) are corresponding angles (from the second blank analysis), so they are congruent.

Step2: Use congruence to find measure

If \(\angle PQR = 60^\circ\) (from diagram context), then \(\angle QHJ=\angle PQR = 60^\circ\) (by congruent corresponding angles property).

Answer:

for the measure:
\(60\)