Since m < 5 = 63°, and m< 5 and m < 1 are congruent because they are corresponding angles:
Then it means that you can use the value of m< 1 to find what the measure of m < 2 is by using the formula:
m < 1 + m< 2 = 180°
Plug in the values into the equation:
63° + m< 2 = 180°
Subtract 63° from both sides:
63° - 63° + m< 2 = 180° - 63°
m < 2 = 117°
By definition, two angles are vertical angles if they are opposite angles formed by the intersection of two lines. Vertical angles are congruent.
m < 1 and m < 3 matches the definition for vertical angles. Thus, to find the measure of m < 3, since m < 1 = 63°, and m < 1 and m < 3 are vertical angles, then it means that they are congruent and have the same measure.
Therefore:
m < 2 = 117°
m < 3 = 63°.
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