The Understanding angles exercise is under the 5th grade (U.S.) Math Mission and Geometry Math Mission. This exercise helps to understand measurements of angles including reflex angles.

Types of Problems

There are four types of problems in this exercise:

  1. Degrees in fraction of a circle: This problem has a circle cut into a number of sectors. The user is expected to answers the fraction of the circle that one sector represents and the measure of it's central angle.

    Degrees in fraction of a circle

  2. Angle description: This problem has describes a situation and asks the user to select the multiple choice selection that is similar to the described situation.

    Angle description

  3. Put in order: This problem has drawings of several angles and the users are asked to put them in order.

    Put in order

  4. Word problem: This problem describes a word problem, sometimes with and sometimes without a picture, and the users are supposed to solve the problem and type the answer in the box.

    Word problem


This exercise is difficult to get accuracy badges because some of the questions can be very subtle. Once every 25 problems or so is a problem that makes sense when user thinks about it but is very easy to misinterpret. Speed badges should also be considered hard at this time.

  1. In the first problem type the answer for the number of degrees will be an integer, so this restricts the possibilities.
  2. The types of angles are:
    1. Acute angle: {1^\circ} to {89^\circ}
    2. Right angle: {90^\circ}
    3. Obtuse angle: {91^\circ} to {179^\circ}
    4. Straight angle: {180^\circ}
    5. Reflex angle (not needed in this exercise): anywhere above {181^\circ}
  3. Put in order always seems to be smallest angle to largest angle.

Real-life Applications

  1. Engineers and architects use angles for designs, roads, buildings and sporting facilities.
  2. Athletes use angles to enhance their performance.
  3. Carpenters use angles to make chairs, tables and sofas.
  4. Artists use their knowledge of angles to sketch portraits and paintings.

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