Add and Subtract Angle Measures - 4th Grade Math

1. What equation represents a whole angle of $150^\circ$ split into $x^\circ$ and $40^\circ$?

   $x+40=150$. The sum of parts equals the whole angle measure.

2. Which expression represents the whole angle if parts measure $a^\circ$, $b^\circ$, and $c^\circ$?

   $a^\circ+b^\circ+c^\circ$. Add all angle measures to find the whole angle measure.

3. Which expression gives the missing part when whole is $W^\circ$ and known part is $K^\circ$?

   $W-K$. Subtract known part from whole to find missing part.

4. Which equation correctly finds $x$ if the whole is $95^\circ$ and parts are $x$ and $28^\circ$?

   $x+28^\circ=95^\circ$. Shows the two parts add up to the whole angle.

5. What is the missing angle if $m\angle AOB=90^\circ$ and $m\angle AOC=32^\circ$ with $C$ inside the angle?

   $m\angle COB=58^\circ$. Subtract: $90^\circ - 32^\circ = 58^\circ$.

6. What rule states how to find a whole angle when it is split into non-overlapping parts?

   Angle addition: $m\angle\text{whole}=m\angle^1+m\angle^2+\cdots$. When an angle is split into parts, add all part measures to get the whole.

7. What is $m\angle AOB$ if it is split into $30^\circ$ and $45^\circ$ parts?

   $75^\circ$. Add the two parts: $30^\circ + 45^\circ = 75^\circ$.

8. What is the whole angle if it is split into $x^\circ$ and $x^\circ$ and $x=38$?

   $76^\circ$. Two equal parts: $38^\circ + 38^\circ = 76^\circ$.

9. What equation represents a whole angle made of three adjacent angles $a$, $b$, and $c$?

   $a+b+c=$ (whole angle measure). Three adjacent angles sum to form the whole angle.

10. What is the sum of the parts if an angle is decomposed into $15^\circ$, $25^\circ$, and $60^\circ$?

    $100^\circ$. Add all parts: $15^\circ + 25^\circ + 60^\circ = 100^\circ$.

11. What is $x$ if the whole is $140^\circ$ and the parts are $2x^\circ$ and $40^\circ$?

    $50^\circ$. Solve $2x + 40 = 140$, so $2x = 100$ and $x = 50$.

12. What is the equation for $x$ if the whole angle is $150^\circ$ and parts are $x$, $35^\circ$, and $40^\circ$?

    $x+35^\circ+40^\circ=150^\circ$. Set up the equation by adding all parts equal to the whole angle.

13. What is $x$ if the whole angle is $90^\circ$ and it is split into $x$ and $x$?

    $x=45^\circ$. Two equal parts make $90^\circ$, so each is $45^\circ$.

14. What does "non-overlapping parts" mean when an angle is split into smaller angles?

    The parts share only a side; their interiors do not cover the same region. Adjacent angles touch at a ray but don't overlap inside.

15. What is the missing part if the whole is $90^\circ$ and the other part is $27^\circ$?

    $63^\circ$. Subtract from right angle: $90^\circ - 27^\circ = 63^\circ$.

16. What is $x$ if an angle is split into $x^\circ$, $25^\circ$, and $35^\circ$ with total $100^\circ$?

    $40^\circ$. Solve $x + 25 + 35 = 100$, so $x = 40$.

17. What is the missing part if the whole is $180^\circ$ and the other part is $115^\circ$?

    $65^\circ$. Subtract from straight angle: $180^\circ - 115^\circ = 65^\circ$.

18. Identify the correct equation if the whole is $y^\circ$ and the two parts are $38^\circ$ and $x^\circ$.

    $38^\circ+x^\circ=y^\circ$. The sum of parts equals the whole angle.

19. What must be true about the parts for angle measures to add (overlapping or non-overlapping)?

    They must be non-overlapping parts. Parts can't share any common interior to add their measures.

20. What is $x$ if $x+25^\circ+40^\circ=120^\circ$?

    $x=55^\circ$. Combine known parts, then subtract from whole: $120° - 65° = 55°$.

21. What is the unknown part if the whole angle is $120^\circ$ and one part is $45^\circ$?

    $75^\circ$. Subtract the known part: $120^\circ - 45^\circ = 75^\circ$.

22. What is $x$ if $x+35^\circ=90^\circ$?

    $x=55^\circ$. Subtract $35°$ from both sides to isolate $x$.

23. What is the whole angle measure if its parts are $15^\circ$, $35^\circ$, and $50^\circ$?

    $100^\circ$. Sum all three parts: $15° + 35° + 50° = 100°$.

24. What is $x$ if $30^\circ+x+20^\circ=90^\circ$?

    $x=40^\circ$. Combine known parts, then subtract from whole: $90° - 50° = 40°$.

25. What is $m\angle AOC$ if $m\angle AOB=25^\circ$ and $m\angle BOC=65^\circ$?

    $90^\circ$. Add the two adjacent angles: $25^\circ + 65^\circ = 90^\circ$.

26. What is $x$ if an angle is split into $x$, $x+10^\circ$, and $30^\circ$ and the whole is $120^\circ$?

    $x=40^\circ$. Solve $x + (x+10^\circ) + 30^\circ = 120^\circ$: $2x + 40^\circ = 120^\circ$.

27. What is the whole angle measure if its parts are $25^\circ$ and $40^\circ$?

    $65^\circ$. Add the non-overlapping parts: $25° + 40° = 65°$.

28. What is the total measure if an angle is decomposed into $20^\circ$, $30^\circ$, and $40^\circ$?

    $90^\circ$. Sum all parts: $20^\circ + 30^\circ + 40^\circ = 90^\circ$.

29. Which equation correctly finds $x$ if the whole is $140^\circ$ and parts are $50^\circ$, $x$, $30^\circ$?

    $50^\circ+x+30^\circ=140^\circ$. Shows the sum of all parts equals the whole angle.

30. What is $x$ if adjacent angles are $x$, $x$, and $20^\circ$, and together they make $100^\circ$?

    $x=40^\circ$. Solve $x + x + 20^\circ = 100^\circ$: $2x = 80^\circ$, so $x = 40^\circ$.

31. What does "non-overlapping parts" mean when an angle is decomposed?

    The parts share a vertex and side, but their interiors do not overlap. Adjacent angles touch at a common ray but don't overlap inside.

32. What is the unknown part if the whole is $75^\circ$ and the known part is $18^\circ$?

    $57^\circ$. Subtract the known from the whole: $75^\circ - 18^\circ = 57^\circ$.

33. What is $x$ if a $150^\circ$ angle is split into $45^\circ$, $x$, and $60^\circ$?

    $x=45^\circ$. Subtract known parts from whole: $150° - 45° - 60° = 45°$.

34. What is $x$ if $70^\circ+x=180^\circ$?

    $x=110^\circ$. Subtract $70°$ from both sides to isolate $x$.

35. What is the measure of each part if a $100^\circ$ angle is split into two equal non-overlapping angles?

    $50^\circ$ each. Divide equally: $100^\circ \div 2 = 50^\circ$.

36. What is the unknown if $m\angle AOB=x^\circ$, split into $x^\circ=3\times 10^\circ+5^\circ$?

    $35^\circ$. Calculate: $3 \times 10^\circ + 5^\circ = 35^\circ$.

37. What is the missing part if a whole angle is $120^\circ$ and one part is $50^\circ$?

    $70^\circ$. Subtract the known part from the whole: $120^\circ - 50^\circ = 70^\circ$.

38. What rule describes the measure of a whole angle split into non-overlapping parts?

    Whole angle measure equals the sum of the part measures. When an angle is decomposed, its parts add up to the whole.

39. What is $x$ if an angle is split into $x$ and $35^\circ$ and the whole is $90^\circ$?

    $x=55^\circ$. Solve $x + 35^\circ = 90^\circ$ by subtracting $35^\circ$ from both sides.

40. What is $x$ if the whole angle is $150^\circ$ and parts are $x$, $35^\circ$, and $40^\circ$?

    $x=75^\circ$. Solve: $x + 35^\circ + 40^\circ = 150^\circ$, so $x = 75^\circ$.

41. What is the value of $x$ if a whole angle is $90^\circ$ and one part is $35^\circ$?

    $x=55^\circ$. Subtract the known part from the whole: $90° - 35° = 55°$.

42. What is $x$ if a straight angle $180^\circ$ is decomposed into three equal angles $x$, $x$, and $x$?

    $x=60^\circ$. Three equal parts sum to $180°$, so each is $180° ÷ 3 = 60°$.

43. What is the measure of the whole angle if parts are $35^\circ$ and $55^\circ$?

    $90^\circ$. Add the parts: $35^\circ + 55^\circ = 90^\circ$.

44. What is $x$ if a $120^\circ$ angle is split into $50^\circ$, $x$, and $30^\circ$?

    $x=40^\circ$. Subtract known parts from whole: $120° - 50° - 30° = 40°$.

45. What is $m\angle AOB$ if $m\angle AOC=140^\circ$ and $m\angle BOC=55^\circ$ (with $B$ between $A$ and $C$)?

    $85^\circ$. Subtract the part from the whole: $140^\circ - 55^\circ = 85^\circ$.

46. What equation represents a whole angle made of two adjacent angles $a$ and $b$?

    $a+b=$ (whole angle measure). Adjacent angles combine by adding their measures.

47. What is $x$ if the whole angle is $180^\circ$ and it is split into $x$ and $65^\circ$?

    $x=115^\circ$. Subtract: $180^\circ - 65^\circ = 115^\circ$.

48. What is $x$ if $m\angle AOC=95^\circ$ and it is decomposed into $m\angle AOB=3x$ and $m\angle BOC=20^\circ$?

    $x=25^\circ$. Solve $3x + 20^\circ = 95^\circ$: $3x = 75^\circ$, so $x = 25^\circ$.

49. What is $x$ if the whole is $110^\circ$ and the parts are $x^\circ$, $x^\circ$, and $30^\circ$?

    $40^\circ$. Solve $x + x + 30 = 110$, so $2x = 80$ and $x = 40$.

50. What is the value of $x$ if a whole angle is $180^\circ$ and the other part is $120^\circ$?

    $x=60^\circ$. Subtract the known part from the whole: $180° - 120° = 60°$.

51. What is $m\angle BOC$ if $m\angle AOC=110^\circ$ and $m\angle AOB=45^\circ$?

    $65^\circ$. Subtract: $110^\circ - 45^\circ = 65^\circ$.

52. Identify the missing angle: whole is $160^\circ$, parts are $75^\circ$, $x$, and $25^\circ$.

    $x=60^\circ$. Subtract known parts from whole: $160° - 75° - 25° = 60°$.

53. What is the total if adjacent non-overlapping angles are $12^\circ$, $18^\circ$, and $60^\circ$?

    $90^\circ$. Add all adjacent angles: $12^\circ + 18^\circ + 60^\circ = 90^\circ$.

54. What rule lets you add measures of non-overlapping parts to get the whole angle?

    Angle addition: $m\angle AOB=m\angle AOC+m\angle COB$. When angles share only a side, their measures add to give the whole.

55. Identify the missing angle: whole is $100^\circ$, parts are $35^\circ$, $x$, and $15^\circ$.

    $x=50^\circ$. Subtract known parts from whole: $100° - 35° - 15° = 50°$.

56. What is the missing angle if the whole is $160^\circ$ and two parts are $45^\circ$ and $70^\circ$?

    $45^\circ$. Subtract sum of known parts: $160^\circ - 45^\circ - 70^\circ = 45^\circ$.

57. What is $x$ if an angle is split into $2x$ and $40^\circ$ and the whole is $100^\circ$?

    $x=30^\circ$. Solve $2x + 40^\circ = 100^\circ$: $2x = 60^\circ$, so $x = 30^\circ$.

58. What is $x$ if $m\angle AOB=200^\circ$ is split into $120^\circ$ and $x^\circ$?

    $80^\circ$. Subtract the known part: $200^\circ - 120^\circ = 80^\circ$.

59. What is $x$ if a right angle $90^\circ$ is decomposed into two equal angles $x$ and $x$?

    $x=45^\circ$. Two equal parts sum to $90°$, so each is $90° ÷ 2 = 45°$.

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