Quiz Answer Explanations

Name:

Date:

I can: solve for unknowns using complementary, supplementary, vertical, linear pair, and angle bisector relationships.

Success criteria: set up an equation from the angle relationship, solve for the variable, and state each requested angle measure.

Differentiation strategies: provide equation templates, step-by-step prompts, or allow a calculator. Extension: create and solve a system for intersecting transversals. Dyslexia-friendly: read-aloud, colored overlays, enlarged text.

📚 Part 1: Multiple Choice — Answers & Explanations

1. If two angles are complementary and one angle measures 35°, what is the measure of the other angle?

55°

145°

35°

90°

Answer: 55°. Explanation: Complementary angles add to 90°. So other angle = 90° − 35° = 55°.

2. Two angles form a linear pair. Their measures are (3x + 10)° and (2x + 30)°. What is x?

x = 10

x = 20

x = 40

x = 60

Answer: x = 28. Explanation: Linear pair angles are supplementary: (3x+10)+(2x+30)=180 → 5x+40=180 → 5x=140 → x=28.

3. If two vertical angles have measures (4y + 5)° and (2y + 25)°, what is y?

y = 5

y = 10

y = 20

y = 15

Answer: y = 10. Explanation: Vertical angles are congruent: 4y+5 = 2y+25 → 2y = 20 → y = 10.

4. Check all statements that are ALWAYS true about vertical angles:

They are congruent (equal in measure)

They are adjacent

They add to 180°

They share a common vertex but not a common side

Answers: "They are congruent" and "They share a common vertex but not a common side." Explanation: Vertical angles are equal and meet at the same vertex; they are not adjacent (they do not share a side) and do not necessarily add to 180°.

✏️ Part 2: Short Answers — Work & Explanations

5. Supplementary angles measure (5x + 10)° and (2x + 40)°. Find x, then find each angle measure. Show work.

Set sum = 180: (5x+10)+(2x+40)=180

7x + 50 = 180 → 7x = 130 → x = 130/7

Angle 1 = 5x+10 = 5*(130/7)+10 = 650/7 + 10 = 720/7 ≈ 102.857°

Angle 2 = 2x+40 = 2*(130/7)+40 = 260/7 + 40 = 540/7 ≈ 77.143°

Explanation: The two angles sum to 180°, solve for x, then substitute to get each measure (exact fractions shown).

6. An angle is bisected. The whole angle measures (3x + 20)°, and each resulting angle measures (2x + 5)°. Find x and the measure of the whole angle.

Bisected means each piece = half the whole: 2*(2x+5) = 3x+20

4x + 10 = 3x + 20 → x = 10

Whole angle = 3x+20 = 3(10)+20 = 50°; each = 2(10)+5 = 25°

Explanation: Doubling a bisected piece equals the whole; solve and substitute.

7. Two vertical angles measure (6x − 12)° and (3x + 30)°. Solve for x and state the measure of each angle.

Vertical angles are equal: 6x − 12 = 3x + 30

3x = 42 → x = 14

Each angle = 6(14) − 12 = 84 − 12 = 72°

Explanation: Set the expressions equal (vertical angles are congruent) and solve.

8. Two adjacent angles form a right angle (90°). Their measures are (x + 12)° and (2x − 8)°. Find x and each angle measure.

They sum to 90: (x+12)+(2x−8)=90

3x + 4 = 90 → 3x = 86 → x = 86/3

Angle 1 = x+12 = 86/3 + 12 = 122/3 ≈ 40.667°

Angle 2 = 2x−8 = 2*(86/3) − 8 = 148/3 ≈ 49.333°

Explanation: Adjacent angles that form a right angle sum to 90°; solve then compute each measure (exact fractions given).

9. A straight line creates two adjacent angles measured (4x + 15)° and (3x + 30)°. Use the angle relationship to find x and list the two angle measures.

Angles on a straight line are supplementary: (4x+15)+(3x+30)=180

7x + 45 = 180 → 7x = 135 → x = 135/7

Angle 1 = 4x+15 = 4*(135/7)+15 = 645/7 ≈ 92.143°

Angle 2 = 3x+30 = 3*(135/7)+30 = 615/7 ≈ 87.857°

Explanation: Supplementary angles along a straight line add to 180°; solve for x and substitute for each measure.