1. Which of the following pairs of angles are supplementary? (Choose all that apply.)
A. 45 degrees and 45 degrees
B. 72 degrees and 100 degrees
C. 35 degrees and 55 degrees
D. 60 degrees and 120 degrees Correct
Explanation
Supplementary angles sum to 180 degrees. Steps: 1) Pair A: 45 + 45 = 90, not 180. 2) Pair B: 72 + 100 = 172, not 180. 3) Pair C: 35 + 55 = 90, not 180. 4) Pair D: 60 + 120 = 180, supplementary, correct.
2. Identify which of the following is a property of a right triangle.
A. The hypotenuse is the side opposite from the right angle Correct
B. The three angles add to 90 degrees
C. The triangle has three sides, which are all considered legs
D. The hypotenuse equals the sum of the legs
Explanation
A right triangle has one 90-degree angle. Steps: 1) Option A: Hypotenuse is opposite the 90-degree angle, correct. 2) Option B: Angles sum to 180 degrees, not 90. 3) Option C: Two sides are legs, one is hypotenuse, not all legs. 4) Option D: Hypotenuse is square root of (leg1 squared + leg2 squared), not leg1 + leg2.
3. Identify which of the following measurements form a right triangle, given the possible lengths of all three sides
A. 4, 9, 16
B. 12, 14, 26
C. 3, 4, 2005 Correct
D. 4, 7, 10
Explanation
Right triangle follows a squared + b squared = c squared, c longest. Steps: 1) Option A: 4 squared + 9 squared = 16 + 81 = 97, not 16 squared = 256. 2) Option B: 12 squared + 14 squared = 144 + 196 = 340, not 26 squared = 676. 3) Option C: 3 squared + 4 squared = 9 + 16 = 25 = 5 squared, correct. 4) Option D: 4 squared + 7 squared = 16 + 49 = 65, not 10 squared = 100.
4. A circle has a radius of 4.5 cm. What is the area of the circle?
A. 28.26 cm squared
B. 31.79 cm squared Correct
C. 15.90 cm squared
D. 63.59 cm squared
Explanation
Circle area is pi times radius squared, pi = 3.14. Steps: 1) Radius = 4.5 cm, 4.5 squared = 20.25. 2) Area = 3.14 times 20.25 = 63.585 cm squared. 3) Round to 63.59 cm squared, correct. Option A uses radius=3, C is half, D is double.
5. A circle has an area of 226.865 in squared. Assume pi=3.14. Find the radius of the circle.
A. 15.05 m
B. 10.05 m
C. 8.50 in Correct
D. 14.17 km
Explanation
Area = pi times radius squared, so radius = square root of (area/pi). Steps: 1) Area = 226.865 in squared, pi = 3.14. 2) radius squared = 226.865 / 3.14 = 72.25. 3) radius = square root of 72.25 = 8.5 in, correct. Options A, B, D use wrong units or values.