Let’s solve each problem step by step.
---
Problem 1:
We are told the figure is a parallelogram. In a parallelogram, opposite sides are equal in length.
Looking at the diagram:
- Side FE = 17
- Side GD = 2x - 5
Since FE and GD are opposite sides, they must be equal:
→ 2x - 5 = 17
Add 5 to both sides:
→ 2x = 22
Divide by 2:
→ x = 11
✔ Check: 2(11) - 5 = 22 - 5 = 17 → matches FE. Correct.
Answer for #1:
B (11)
---
Problem 2:
Again, it’s a parallelogram. In a parallelogram, consecutive angles are supplementary — meaning they add up to 180°.
In the diagram:
- Angle Q = 80°
- Angle R = 14x + 2
Angles Q and R are consecutive (next to each other), so:
→ 80 + (14x + 2) = 180
Simplify:
→ 14x + 82 = 180
Subtract 82 from both sides:
→ 14x = 98
Divide by 14:
→ x = 7
✔ Check: 14(7) + 2 = 98 + 2 = 100; 80 + 100 = 180 → correct.
Answer for #2:
C (7)
---
Problem 3:
“Parallelograms are ...”
A parallelogram is a four-sided shape with opposite sides parallel. So it’s a type of quadrilateral.
Options:
A. pentagons → 5 sides → no
B. quadrilaterals → 4 sides → yes
C. hexagons → 6 sides → no
D. triangles → 3 sides → no
Answer for #3:
B (quadrilaterals)
---
Problem 4:
It’s a parallelogram. We’re given angle C = 132°, and we need to find angle A (labeled as 2x).
In a parallelogram, opposite angles are equal.
Angle A and angle C are opposite → so angle A = angle C = 132°
But angle A is labeled as 2x → so:
→ 2x = 132
Divide by 2:
→ x = 66
✔ Check: 2 × 66 = 132 → matches angle C. Correct.
Answer for #4:
C (66)
---
Problem 5:
“The opposite angles of a parallelogram are ...”
From geometry rules: Opposite angles in a parallelogram are equal → which means they are congruent.
Options:
A. complementary → adds to 90° → no
B. congruent → equal → yes
C. perpendicular → forms 90° angles → not about angles being equal
D. supplementary → adds to 180° → that’s for consecutive angles, not opposite
Answer for #5:
B (congruent)
---
Final Answers:
1. B
2. C
3. B
4. C
5. B
Parent Tip: Review the logic above to help your child master the concept of geometry worksheet 9th grade.
