Question

7 multiple - choice 2 points
tonya created the following design for her geometry project.
what kind of angles are ∠acd and ∠bce?
interior angles
complementary angles
supplementary angles
vertical angles
8 multiple - choice 2 points
andrew constructed a triangle so that ∠1 and ∠2 were the same size and ∠3 measured 80°.

Explanation:

Step1: Recall angle - type definitions

Interior angles are angles inside a polygon. Complementary angles add up to 90°. Supplementary angles add up to 180°. Vertical angles are opposite each other when two lines intersect.

Step2: Analyze ∠ACD and ∠BCE

∠ACD and ∠BCE are formed by the intersection of two lines. They are opposite each other. So they are vertical angles.

Step3: Solve for angles in the triangle

The sum of the interior angles of a triangle is 180°. Let ∠1 = ∠2=x. Then x + x+80° = 180°. Combining like - terms gives 2x=180° - 80° = 100°. Dividing both sides by 2, we get x = 50°.

Answer:

1. D. vertical angles
2. 50°