Angles 1 and 7 are corresponding, both 32 degrees. Angles 2 and 8 are vertical, both x degrees. Angle 2 is 32 degrees. Using the angle interior sum property, angle 1 is 116 degrees. Angle 3 cannot be determined. Angle 7 is 32 degrees. The correct answers are A. 116 degrees, B. 32 degrees, C. Cannot be determined, D. 32 degrees.
1. Identify corresponding angles:
Angles 1 and 7: These are corresponding angles because they are on opposite sides of the transversal and outside the parallel lines. Since parallel lines never intersect, corresponding angles are always congruent. Therefore, if angle 5 is 32 degrees, then angle 7 is also 32 degrees.
2. Identify vertical angles:
Angles 2 and 8: These are vertical angles because they share the same vertex and are opposite each other. Vertical angles are always congruent, so if angle 2 is x degrees, then angle 8 is also x degrees.
3. Use the angle interior sum property:
The angle interior sum property states that the sum of the angles in a triangle is equal to 180 degrees. You can use this property to find the measures of missing angles in triangles.
4. Solve for the missing angles:
Angle 2: Since angles 2 and 8 are vertical angles and angle 8 is 32 degrees (because it is corresponding to angle 5), then angle 2 is also 32 degrees.
Angle 1: We know that angle 5 is 32 degrees and angle 7 is also 32 degrees (because they are corresponding angles). Together, these two angles form part of a triangle with angle 1. Since the sum of the angles in a triangle is 180 degrees, we can set up an equation: angle 5 + angle 7 + angle 1 = 180 degrees. Substituting the known values, we get 32 degrees + 32 degrees + angle 1 = 180 degrees. Solving for angle 1, we get angle 1 = 116 degrees.
Therefore, the measures of the other angles are:
A. M angle 1 = 116 degrees
B. M angle 2 = 32 degrees
C. M angle 3 = Cannot be determined from the given information
D. M angle 7 = 32 degrees