Question

Lian draws three lines on the board. Lines m and n are parallel. Lian says that the measure of <2 is 2··3 the measure of <1. What is the measure of <2?

Answer 1

Using the property of interior angles on same sides

2x−8+3x−7=180

5x−15=180

x=39

∘

2x−8=2×39−8=70

3x−7=3×39−7=110

Answer 2

Answer:

When two lines are parallel, any pair of alternate interior angles are congruent. In other words, if line m is parallel to line n, then <2 and <3 are congruent.

Step-by-step explanation:

• If Lian says that the measure of <2 is 2 times the measure of <1, we can set up an equation: <2 = 2*<1.
• We can use the fact that <2 and <3 are congruent to substitute <3 for <2 in the equation: <3 = 2*<1.
• Since <2 and <3 are congruent, we can use the equation <3 = 2*<1 to find the measure of <2. If <3 is equal to 2 times <1, then <2 must also be equal to 2 times <1.
• Therefore, the measure of <2 is also 2 times the measure of <1.
• To find the specific measure of <2, we would need to know the measure of <1. Without that information, we cannot determine the measure of <2.

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