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Lines, Angles, and Triangles

Math · Geometry and Trigonometry · 49 questions · every one comes with a full explanation.

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  1. 1Triangle upper A upper C upper D partially overlaps triangle upper E upper B upper D. Point upper C is on line segment upper B upper D. Point upper E is on line segment upper A uppHard · Geometry and Trigonometry
  2. 2From left to right, horizontal line segment upper P upper V includes the following points: Upper P Upper Q Upper R Upper S Upper T Upper V Points upper X and upper U are each belHard · Geometry and Trigonometry
  3. 3What is the value of x ?Hard · Geometry and Trigonometry
  4. 4Clockwise from top left, the 3 lines are labeled t, m, and n. Line t intersects both line m and line n. At the intersection of line t and line m, 1 angle is labeled clockwise from Easy · Geometry and Trigonometry
  5. 5In the given triangle, and has a measure of . What is the value of x ?Easy · Geometry and Trigonometry
  6. 6In the figure above, and intersect at point P, , and . What is the measure, in degrees, of ? (Disregard the degree symbol when gridding your answer.)Hard · Geometry and Trigonometry
  7. 7Right triangle upper P upper Q upper R is labeled as follows: Angle upper R is a right angle. Right triangle upper S upper T upper U is labeled as follows: Angle upper U is a riEasy · Geometry and Trigonometry
  8. 8Clockwise from top left, the 3 lines are labeled s, q, and r. Line s intersects both line q and line r. At the intersection of line s and line q, 1 angle is labeled clockwise from Medium · Geometry and Trigonometry
  9. 9In the figure above, lines and m are parallel, , and . What is the value of x ?Easy · Geometry and Trigonometry
  10. 10In the figure above, , , and are parallel. Points B and E lie on and , respectively. If , and , what is the length of , to the nearest tenth?Medium · Geometry and Trigonometry
  11. 11In triangle A B C , the measure of angle B is 90° and BD is an altitude of the triangle. The length of AB is 15 and the length of AC is 23 greater than the length of AB. WhHard · Geometry and Trigonometry
  12. 12In △XYZ, the measure of ∠X is 24 ° and the measure of ∠Y is 98 °. What is the measure of ∠Z?Easy · Geometry and Trigonometry
  13. 13Two nearby trees are perpendicular to the ground, which is flat. One of these trees is 10 feet tall and has a shadow that is 5 feet long. At the same time, the shadow of the otheMedium · Geometry and Trigonometry
  14. 14Clockwise from top left, the 3 lines are labeled t, m, and n. Line t intersects both line m and line n. At the intersection of line t and line m, 1 angle is labeled clockwise from Easy · Geometry and Trigonometry
  15. 15In triangles A B C and D E F , angles B and E each have measure 27° and angles C and F each have measure 41°. Which additional piece of information is sufficient to Hard · Geometry and Trigonometry
  16. 16In triangles L M N and R S T , angles L and R each have measure 60 °, L N = 10 , and R T = 30 . Which additional piece of information is sufficientHard · Geometry and Trigonometry
  17. 17Triangles ABC and DEF are shown above. Which of the following is equal to the ratio ?Medium · Geometry and Trigonometry
  18. 18In the figure above, what is the length of ?Hard · Geometry and Trigonometry
  19. 19Triangle X Y Z is similar to triangle R S T such that X , Y , and Z correspond to R , S , and T , respectively. The measure of ∠Z is 20 ° and 2 X Y = R S Hard · Geometry and Trigonometry
  20. 20Clockwise from top left, the 3 lines are labeled m, r, and s. Line m intersects both line r and line s. At the intersection of line m and line r, 1 angle is labeled clockwise from Medium · Geometry and Trigonometry
  21. 21Triangle A B C is similar to triangle X Y Z , such that A , B , and C correspond to X , Y , and Z respectively. The length of each side of triangle X Y Z is 2 tMedium · Geometry and Trigonometry
  22. 22In △XYZ, the measure of ∠X is 23 ° and the measure of ∠Y is 66 °. What is the measure of ∠Z?Easy · Geometry and Trigonometry
  23. 23Clockwise from top left, the lines are labeled t, m, and n. Line t intersects both line m and line n. At the intersection of line t and line m, 1 angle is labeled clockwise from toEasy · Geometry and Trigonometry
  24. 24In triangle JKL, the measures of ∠K and ∠L are each 48°. What is the measure of ∠J, in degrees? (Disregard the degree symbol when entering your answer.)Medium · Geometry and Trigonometry
  25. 25Quadrilateral P'Q'R'S' is similar to quadrilateral P Q R S , where P , Q , R , and S correspond to P', Q', R', and S', respectively. The measure of angle P is 30°, the measMedium · Geometry and Trigonometry
  26. 26At a certain time and day, the Washington Monument in Washington, DC, casts a shadow that is 300 feet long. At the same time, a nearby cherry tree casts a shadow that is 16 feet loEasy · Geometry and Trigonometry
  27. 27In the figure above, intersects at C. If , what is the value of y ?Easy · Geometry and Trigonometry
  28. 28In triangle ABC, the measure of angle A is . If triangle ABC is isosceles, which of the following is NOT a possible measure of angle B ?Medium · Geometry and Trigonometry
  29. 29In the figure above, . What is the value of x ?Hard · Geometry and Trigonometry
  30. 30Clockwise from top left, the 3 lines are labeled t, m, and n. Line t intersects both line m and line n. At the intersection of line t and line m, 2 angles are labeled clockwise froMedium · Geometry and Trigonometry
  31. 31The area of triangle ABC above is at least 48 but no more than 60. If y is an integer, what is one possible value of x ?Hard · Geometry and Trigonometry
  32. 32In the triangle above, . What is the value of b ?Easy · Geometry and Trigonometry
  33. 33In the figure, three lines intersect at point P. If and , what is the value of z ?Easy · Geometry and Trigonometry
  34. 34Clockwise from top left, the 3 lines are labeled l, m, and n. Line l intersects both line m and line n. At the intersection of line l and line m, 1 angle is labeled clockwise from Easy · Geometry and Trigonometry
  35. 35In the figure above, lines and k are parallel. What is the value of a ?Easy · Geometry and Trigonometry
  36. 36In triangle A B C , the measure of angle B is 52° and the measure of angle C is 17°. What is the measure of angle A ?Easy · Geometry and Trigonometry
  37. 37Triangle ABC and triangle DEF are shown. The relationship between the side lengths of the two triangles is such that . If the measure of angle BAC is 20°, what is the measure, in dMedium · Geometry and Trigonometry
  38. 38In the given figure, extends to point D. If the measure of is equal to the measure of , what is the value of x ?Easy · Geometry and Trigonometry
  39. 39Clockwise from top left, the 3 lines are labeled t, j, and k. Line t intersects both line j and line k. At the intersection of line t and line j, 2 angles are labeled clockwise froEasy · Geometry and Trigonometry
  40. 40In triangle RST, angle T is a right angle, point L lies on RS¯, point K lies on ST¯, and LK¯ is parallel to RT¯. If the length of RT¯ is 72 units, the length of LK¯ is 24 unitHard · Geometry and Trigonometry
  41. 41Clockwise from top left, the 3 lines are labeled, c, s, and t. Line c intersects both line s and line t. At the intersection of line c and line s, 1 angle is labeled clockwise fromEasy · Geometry and Trigonometry
  42. 42Triangles A B C and D E F are congruent, where A corresponds to D , and B and E are right angles. The measure of angle A is 18°. What is the measure of angle F ?Easy · Geometry and Trigonometry
  43. 43In the figure above, segments AE and BD are parallel. If angle BDC measures 58° and angle ACE measures 62°, what is the measure of angle CAE ?Medium · Geometry and Trigonometry
  44. 44Counterclockwise from top right, the lines are labeled s, r, q, and t. Line s intersects line r above line q. Line s and line r each intersect line q and line t. At the intersectioHard · Geometry and Trigonometry
  45. 45In the figure above, lines m and n are parallel. What is the value of b ?Easy · Geometry and Trigonometry
  46. 46Right triangles L M N and P Q R are similar, where L and M correspond to P and Q , respectively. Angle M has a measure of 53 °. What is the measure of angle Q ?Medium · Geometry and Trigonometry
  47. 47In a right triangle, the measure of one of the acute angles is 51°. What is the measure, in degrees, of the other acute angle?Easy · Geometry and Trigonometry
  48. 48In the figure above, two sides of a triangle are extended. What is the value of x ?Easy · Geometry and Trigonometry
  49. 49In the figure above, and . What is the length of ?Hard · Geometry and Trigonometry