OAR OAR Math Skills: Geometry 3 — Questions and Answers
Question 1: A triangle has angles measuring 45° and 75°. What is the measure of the third angle?
- 60° (Correct answer)
- 80°
- 120°
- 40°
Correct answer: 60°
The interior angles of a triangle sum to 180°; 180° − 45° − 75° = 60°.
Question 2: A cylinder has radius 3 cm and height 10 cm. What is its volume? (Use π ≈ 3.14)
- 282.6 cm³ (Correct answer)
- 94.2 cm³
- 565.2 cm³
- 188.4 cm³
Correct answer: 282.6 cm³
V = π × r² × h = 3.14 × 9 × 10 = 282.6 cm³.
Question 3: Which of the following best describes a rhombus?
- A parallelogram with all four sides equal (Correct answer)
- A rectangle with all four angles equal
- A trapezoid with one pair of equal sides
- A quadrilateral with no parallel sides
Correct answer: A parallelogram with all four sides equal
A rhombus is a parallelogram where all four sides are congruent, but angles need not be 90°.
Question 4: Point A is at (2, 3) and Point B is at (−2, 6). What is the distance AB?
- 5 (Correct answer)
- 7
- √41
- √7
Correct answer: 5
d = √[(−2−2)² + (6−3)²] = √[16 + 9] = √25 = 5.
Question 5: A square has a diagonal of 8√2 inches. What is the side length of the square?
- 8 in (Correct answer)
- 4√2 in
- 16 in
- 4 in
Correct answer: 8 in
For a square with side s, diagonal = s√2; s = (8√2) ÷ √2 = 8 in.
Question 6: Two angles are vertical angles. One measures 3x + 10 degrees and the other measures 5x − 20 degrees. What is x?
- 15 (Correct answer)
- 20
- 10
- 25
Correct answer: 15
Vertical angles are equal: 3x + 10 = 5x − 20 → 30 = 2x → x = 15.
Question 7: A rectangular room is 12 ft by 15 ft. If you want to place tiles that are each 1.5 ft × 1.5 ft, how many tiles do you need?
- 80 (Correct answer)
- 120
- 60
- 90
Correct answer: 80
Room area = 180 ft²; tile area = 2.25 ft²; tiles = 180 ÷ 2.25 = 80.
OAR OAR Math Skills: Geometry 3
A triangle has angles measuring 45° and 75°.
What is the measure of the third angle?