1. In $\triangle XYZ$, the measure of $\angle X$ is $40°$ and the measure of $\angle Y$ is $70°$. What is the measure of $\angle Z$?
2. In $\triangle ABC$, $AB = 8$, $AC = 12$, and $\angle A = 30°$. What is the area of $\triangle ABC$?
3. Triangle MNO is an equilateral triangle. What is the measure of angle M?
4. A 15-foot ladder is leaning against a vertical wall. The base of the ladder is 9 feet away from the base of the wall on level ground. How high up the wall, in feet, does the ladder reach?
5. In right triangle DEF, angle D is the right angle. If side DE = 3 and side DF = 4, what is the length of side EF?
6. In $\triangle ABC$: $\angle A = 50°$, $\angle B = 60°$, $\angle C = 70°$. What is the correct ordering of side lengths from least to greatest?
7. In rectangle $WXYZ$, the length is 15 cm and the diagonal is 17 cm. What is the width, in cm?
8. In right triangle XYZ, angle X is the right angle. If side XY = 6 and side XZ = 8, what is the length of side YZ?
9. Triangle STU is a 45-45-90 triangle. If the hypotenuse ST is 10, what is the length of each leg?
10. Triangle MNO has sides of lengths 5, 12, and 13. What type of triangle is MNO?
11. In right triangle JKL with right angle at J, if side JK = 9 and side JL = 12, what is the length of hypotenuse KL?
12. In triangle DEF, angle D measures 80° and angle E measures 70°. What is the measure of angle F?
13. In triangle STU, if ST = TU = US, what type of triangle is triangle STU?
14. In a right triangle, one leg measures 3 units and the other leg measures 4 units. What is the length of the hypotenuse?
15. Triangle GHI is a 45-45-90 triangle with legs measuring 5 units each. What is the length of the hypotenuse?
16. In triangle GHI, angle G measures 100° and angle H measures 40°. What is the measure of angle I?
17. In triangle DEF, angle D measures 85°, angle E measures 45°. What is the measure of angle F?
18. In a 45-45-90 triangle, if the hypotenuse measures 10 units, what is the length of one leg?
19. In triangle MNO, angle M measures 120° and angle N measures 30°. What is the measure of angle O?
20. In a right triangle, if one leg measures 9 units and the other leg measures 12 units, what is the length of the hypotenuse?
21. In triangle MNO, angle M measures 45° and angle N measures 45°. What is the measure of angle O?
22. In a right triangle, one leg measures 5 units and the other leg measures 12 units. What is the length of the hypotenuse?
23. In a 45-45-90 triangle, if one leg measures 7 units, what is the length of the hypotenuse?
24. What type of triangle has one angle measuring more than 90°?
25. In triangle JKL, angle J measures 90°, angle K measures 30°. What is the measure of angle L?
26. What type of triangle has two sides of equal length?
27. In a right triangle, one leg measures 8 units and the hypotenuse is 10 units. What is the length of the other leg?
28. In a 30-60-90 triangle, if the shortest side is 4 units, what is the length of the hypotenuse?
29. What type of triangle has all angles equal?
30. In triangle JKL, angle J measures $30^\circ$, angle K measures $60^\circ$. What is the measure of angle L?
31. What type of triangle has all sides of different lengths?
32. Triangle ABC is a 30-60-90 triangle. If side AC (the hypotenuse) is 10, what is the length of side AB (shorter leg)?
33. In right triangle $PQR$, $\angle Q$ is a right angle. The hypotenuse $\overline{PR}$ has length $13$ and one leg $\overline{QR}$ has length $5$. What is the length of the other leg $\overline{PQ}$?
34. In a $30$-$60$-$90$ right triangle, the hypotenuse has length $18$. What is the length of the shortest side (opposite $30^\circ$)?
35. In a $45$-$45$-$90$ right triangle, each leg has length $7$. What is the length of the hypotenuse?
36. A triangle has side lengths $7$, $24$, and $25$. Which describes the triangle?
(Choose from: right, isosceles, equilateral, scalene.)
37. In triangle $ABC$, angles $A$ and $B$ measure $76^\circ$ and $49^\circ$. What is the measure of angle $C$?
38. In the grayscale diagram, triangle $ABC$ is right with a right angle at $B$. The side lengths are labeled $AB=5$, $BC=12$, and $AC=x$. What is the length of side $x$?
(Use $a^2+b^2=c^2$ with $c$ as the hypotenuse.)
39. In right triangle $ABC$, $\angle C$ is a right angle. If $AC=15$ and $BC=8$, what is the length of the hypotenuse $AB$?
40. Triangle $XYZ$ has side lengths $10$, $10$, and $10$. Which describes the triangle?
(Choose from: right, isosceles, equilateral, scalene.)
41. Right triangle $RST$ has a right angle at $S$. If $RS=12$ and the hypotenuse $RT=20$, what is the length of $ST$?
42. A triangle has angles $44^\circ$ and $89^\circ$. What is the measure of the third angle?
43. In a $45$-$45$-$90$ right triangle, the hypotenuse has length $10\sqrt{2}$. What is the length of each leg?
44. A right triangle has legs of lengths $9$ and $12$. What is the hypotenuse of the triangle?
45. Triangle $DEF$ has angles $65^\circ$, $65^\circ$, and $x$. What is the measure of angle $x$?
46. In a $30$-$60$-$90$ right triangle, the shortest side (opposite $30^\circ$) has length $6$. What is the length of the hypotenuse?
47. A triangle has side lengths $5$, $5$, and $8$. Which describes the triangle?
(Choose from: right, isosceles, equilateral, scalene.)
48. A right triangle has hypotenuse length $17$ and one leg length $15$. What is the length of the other leg?
49. If two angles of a triangle measure $38^\circ$ and $90^\circ$, what is the measure of the third angle?
50. Triangle $ABC$ is a right triangle with a right angle at $C$. The legs have lengths $6$ and $8$. What is the length of the hypotenuse $\overline{AB}$?
51. In triangle GHI, angle G measures 45° and angle H measures 45°. What type of triangle is GHI?
52. In triangle VWX, angle V measures 30°, and angle W measures 60°. What is the measure of angle X?
53. If two angles of a triangle measure 45° and 85°, what is the measure of the third angle?
54. A rectangle has a width of 15 cm and a diagonal of 17 cm. What is the area, in square centimeters, of the rectangle?
55. In triangle DEF, the length of side DE is 7 inches and the length of side EF is 12 inches. Which of the following represents all possible lengths, x, in inches, for the third side DF?
56. In triangle ABC, angle A measures 90°. If angle B measures 45°, what is the measure of angle C?
57. In right triangle PQR, angle P is the right angle. If side PQ = 5 and side PR = 12, what is the length of side QR?
58. In a right triangle, the hypotenuse is 15 units and one leg is 9 units. What is the length of the other leg?
59. In triangle PQR, angle P measures 150° and angle Q measures 15°. What is the measure of angle R?
60. Triangle ABC is an isosceles triangle with angles A and B equal. If angle C measures 40°, what is the measure of angle A?
61. In a triangle, two angles measure 45° each. What is the measure of the third angle?