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The topic Solving for unknown angles appears under the 7th grade (U.S.) Math Mission. This exercise takes several diagrams and uses them to find missing angles.

Types of Problems

There are four types of problems in this exercise:

  1. Use AAP or VAT to solve for the variable: This problem provides a sketch of intersecting lines. The student is expected to use the Angle Addition Postulate and Vertical Angles Theorem to solve for x.
    Sfua1

    Use AAP or VAT to solve for the variable

  2. Solve the real-life word problem: This problem involves cutting up a cake or pie. The student is asked to find the measure of the central angle for one of the slices.
    Sfua2

    Solve the real-life word problem

  3. Use the diagram and answer the questions: This problem provides a 2D drawing and has several questions related to it. The student is asked to answer the question correctly.
    Sfua3

    Use the diagram and answer the questions

  4. Solve the problem with no picture: This problem describes two angles whose measures are related in some way. The student is asked to find the measure of one of the angles from the provided information.
    Sfua4

    Solve the problem with no picture

Strategies

Many elements of geometric and algebraic knowledge come together in this exercise.

  1. Sometimes either the AAP or VAT can be used so whichever is faster would help to increase efficiency.
  2. The two angles in the Solve the problem with no picture problem are either complementary or supplementary. Therefore the equation will be to take the descriptions, add them together, and set equal to 90 or 180 as needed.

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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