Question

question 7 (multiple choice worth 1 points) (01.07 mc) chelsea drew two parallel lines, kl and mn, intersected by a transversal pq, as shown below. which fact would help chelsea prove that the measure of angle krp is equal to the measure of angle msr? when angles krs and msr are equal to angle rsn, the angles krp and msr are congruent. when angles krp and krs are equal to angle lrs, the angles krp and msr are congruent. when angle lrs is equal to angle krp and angles lrs and rsn are complementary, angle krp and angle msr are congruent. when angle lrs is equal to both the angles krp and msr, angle krp and angle msr are congruent to each other.

Explanation:

Step1: Recall angle - congruence rules

When two parallel lines are intersected by a transversal, corresponding angles, alternate - interior angles, and alternate - exterior angles are congruent. Here, we need to find a condition for ∠KRP and ∠MSR to be congruent.

Step2: Analyze each option

• Option 1: If ∠KRS = ∠RSN and ∠MSR=∠RSN, it doesn't directly relate ∠KRP and ∠MSR in a way to prove their congruence.
• Option 2: If ∠KRP = ∠LRS and ∠KRS = ∠LRS, it doesn't help in proving ∠KRP = ∠MSR.
• Option 3: If ∠LRS = ∠KRP and ∠LRS+∠RSN = 90°, it doesn't prove ∠KRP = ∠MSR.
• Option 4: If ∠LRS=∠KRP and ∠LRS = ∠MSR, then by the transitive property of equality (if a = b and a = c, then b = c), we can say that ∠KRP=∠MSR.

Answer:

When angle LRS is equal to both the angles KRP and MSR, angle KRP and angle MSR are congruent to each other.