Answer:
m < 2 = 49°
m < 4 = 49°
Step-by-step explanation:
Given that m < 5 = 131°:
< 3 and < 5 are Alternate interior angles, which are angles that do not have a common vertex on alternate sides of the transversal. These angles have the same measure. Therefore, m < 3 = 131°.
Angles < 2 and < 3 are supplementary angles, in which their measures have a sum of 180°. Therefore, to find the measure of angle 2, we can establish the following formula:
m < 2 + m < 3 = 180°
Subtract - m < 3 from both sides to isolate m < 2:
m < 2 + m < 3 - m < 3 = 180°- m < 3
m < 2 = 180°- m < 3
Next, plug in the value of m < 3 into the equation:
m < 2 = 180°- m < 3
m < 2 = 180°- 131°
m < 2 = 49°
Next, m < 2 and m < 4 are vertical angles. Two angles are vertical angles if they are opposite angles formed by the intersection of two lines. Vertical angles are congruent. Since m < 2 = 49°, then m < 4 must also be 49°.
Therefore, m < 2 = 49° and m < 4 = 49°
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