Geometry quiz on quadrilaterals focusing on parallelogram properties and calculations.

Let’s solve each question one by one, based on the properties of parallelograms.

---

Question 1:

> The figure is a parallelogram. Solve for x.
> Side GD = 2x – 5, side FE = 17

✔ Property: In a parallelogram, opposite sides are equal.

So, GD = FE
→ 2x – 5 = 17
Add 5 to both sides:
→ 2x = 22
Divide by 2:
→ x = 11

✔ Answer: B. 11

---

Question 2:

> The figure is a parallelogram. Solve for x.
> Angle Q = 80°, side QR = 14x + 2

Wait — this seems odd. We’re given an angle and a side length, but no direct relationship between them unless there's a typo or mislabeling.

But looking at the diagram (even though it’s not visible), in many such problems, if angle Q is 80°, and we're solving for x in a side expression like 14x + 2, it might be that the side is opposite or adjacent, but no direct geometric property links an angle to a side length without more info.

However, in many multiple-choice quizzes, if they give an angle and ask to solve for x in a side expression, it’s often a trick — perhaps the side is meant to be equal to another side? But here, only one side is labeled.

Alternatively — maybe the label “14x + 2” is actually meant to be an angle? That would make sense.

Let’s assume that “14x + 2” is meant to be the measure of angle R, not a side. Because in a parallelogram:

✔ Consecutive angles are supplementary (add to 180°)

So if angle Q = 80°, then angle R (adjacent) = 180° – 80° = 100°

Set 14x + 2 = 100
→ 14x = 98
→ x = 7

✔ Answer: C. 7

*(This is the most logical interpretation — likely a labeling error where “14x+2” was meant to be an angle, not a side.)*

---

Question 3:

> Parallelograms are ...

✔ A parallelogram is a four-sided polygon → so it is a quadrilateral.

- Pentagon = 5 sides ✘
- Hexagon = 6 sides ✘
- Triangle = 3 sides ✘

✔ Answer: B. quadrilaterals

---

Question 4:

> What is the value of x?
> Angle C = 132°, angle A = 2x

In parallelogram ABCD, opposite angles are equal, and consecutive angles are supplementary.

Angle C and angle A are opposite angles (if labeled in order A-B-C-D).

So angle A = angle C → 2x = 132°
→ x = 66

✔ Answer: C. 66

*(Note: If angle A and angle C were consecutive, they’d add to 180°, but since 2x = 132 gives x=66, and 66×2=132, it matches opposite angles being equal.)*

---

Question 5:

> The opposite angles of a parallelogram are ...

✔ Congruent (equal in measure)

- Complementary = add to 90° ✘
- Perpendicular = refers to lines, not angles ✘
- Supplementary = add to 180° — true for *consecutive* angles, not opposite ✘

✔ Answer: B. congruent

---

## ✔ Final Answers:

1. B. 11
2. C. 7 *(assuming "14x+2" is an angle, not a side)*
3. B. quadrilaterals
4. C. 66
5. B. congruent

Let me know if you want diagrams or further explanation!