Question

Find the measure of each of the numbered angles.

Answer 1

1. 47°
2. 63°
3. 70°
4. 70°
5. 47°

Explanation:

You want to know the measures of the numbered angles in the given parallelogram figure.

Angle relations

There are several relevant angle relations that can be used to answer this question.

• The sum of angles in a triangle is 180°.
• Angles of a linear pair are supplementary.
• Opposite angles in a parallelogram are congruent.
• Alternate interior angles at a transversal are congruent.
• Corresponding angles at a transversal are congruent.

∠1

The sum of the two angles that make up the corner angle D is the same as the exterior angle at E.

∠1 +63° = 110°

∠1 = 47° . . . . . . . . subtract 63°

∠2

The angle marked 63° and angle 2 are alternate interior angles, so congruent.

∠2 = 63°

∠3

The two angles at E are a linear pair:

∠3 = 180° -110°

∠3 = 70°

∠4

Angle 4 is opposite angle 3 in the parallelogram, so is congruent to it.

∠4 = 70°

∠5

Angle 5 is an alternate interior angle with respect to angle 1, so is congruent to it.

∠5 = 47°