Question

Find the measure of each angle. Assume the lines are parallel, I dont have a protractor small enough to do this job.

m∠2 = __°.

m∠3 = __°.

m∠4 = __°.

m∠5 = __°.

m∠6 = __°.

m∠7 = __°.

m∠8 = __°.

Answer 1

All angles are 113 or 67. See below for each angle measure.

Explanation:

Parallel lines cut by a transversal have several angle relationships which can be used to find an unknown angle measure:

• Alternate Interior Angles are angles across the transversal between pairs of parallel lines. These angles are congruent. Example: 8 and 4 are congruent and are pairs of alternate interior angles. 7 and 3 are another set.

• Alternate Exterior Angles are angles across the transversal outside of the parallel lines. These angles are congruent. Example 1 & 5 are congruent alternate exterior angles. 2 and 6 are another set.

• Supplementary angles are angles which form a line and add to 180. If angle 1 + angle 2 = 180 and angle 1 = 113, then 113 + Angle 2 =180. Angle 2 must be 67 degrees.

• Vertical angles are angles across a vertex. They are congruent. Example: Angle 2 and Angle 8 are both 67.

Using these relationships, the following angles have the following measures:

Angle 1 = 113

Angle 2 = 67

Angle 3 = 113

Angle 4 = 567

Angle 5 =113

Angle 6 = 67

Angle 7 = 113

Angle 8 = 67