The measures of the angles are as follows: option b)
m∠1 = 97°
m∠2 = 114°
m∠3 = 97°
m∠4 = 114°
To find the measures of the angles, let's analyze the given information. We are given that m∠9 is 97° and m∠12 is 114°.
First, let's identify the relationships between the angles in the given diagram. It seems like there are three parallel lines cut by two transversals.
Since angles 9 and 12 are corresponding angles, and corresponding angles are congruent when two parallel lines are cut by a transversal, we can conclude that m∠1 is also 97°.
Similarly, angles 9 and 4 are alternate exterior angles, and alternate exterior angles are congruent when two parallel lines are cut by a transversal. Hence, m∠4 is 114° as well.
To find the measure of m∠2 and m∠3, we need to use the properties of angles formed by parallel lines.
Angle 2 is a corresponding angle to angle 4, so m∠2 = m∠4 = 114°.
Angle 3 is a corresponding angle to angle 9, so m∠3 = m∠9 = 97°.