The measure of ∠2 is 70° .
What is corresponding angles?
The corresponding angles definition tells us that when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other and are equal in measure.
What is supplementary angles angles?
When the sum of two angles is 180°, then the angles are known as supplementary angles. In other words, if two angles add up, to form a straight angle, then those angles are referred to as supplementary angles.
According to the question
line a is parallel to line b and c and d are transversal for them
line c is parallel to line d and a and b are transversal for them
m∠13 = (12x - 22)°
m∠14 = (9x - 29)°
Now
As, ∠13 and ∠14 forms supplementary angles .
i.e
m∠13 + m∠14 = 180°
12x - 22° + 9x - 29° = 180°
21x - 51° = 180°
21x = 180° + 51 °
21x = 231 °
x = 11°
So,
m∠13 = 12*11 - 22° = 110°
m∠14 = 9*11 - 29° = 70°
Now,
according to corresponding angles
m∠14 = m∠6 = m∠2 = 70°
Hence, the measure of ∠2 is 70° .
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