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Find unknown angle measures

Determining an unknown angle measure involves interpreting an angle as a part of a larger angle and using angle addition or subtraction, including relationships involving right angles (90°) and straight angles (180°). The learner represents these relationships in labeled diagrams and solves whole–part problems with whole-number degree measures, understanding that the location or orientation of an angle does not change its measure; formal angle relationships and general algebraic methods beyond these cases are not included.

Detailed Explanation: Find unknown angle measures

An unknown angle is often a missing part of a larger angle.

First, identify:

  • the whole angle
  • the known part
  • the unknown part

Then use:

unknown part=whole angle−known part\text{unknown part}=\text{whole angle}-\text{known part}

Remember that turning an angle in a different direction does not change its measure.

Example

Angle (ABC)(ABC) is a right angle, so its total measure is (90∘)(90^\circ). Ray (BD)(BD) splits it into two angles. One angle measures (35∘)(35^\circ). Find (m∠DBC)(m\angle DBC).

You can picture it like this:

A
 \ 
  \ 35°
   B────────C

  1. The whole angle is a right angle:

m∠ABC=90∘m\angle ABC=90^\circ

  1. The known part is:

35∘35^\circ

  1. The two smaller angles make the whole angle:

35∘+m∠DBC=90∘35^\circ+m\angle DBC=90^\circ

  1. Subtract the known part from the whole:

m∠DBC=90∘−35∘m\angle DBC=90^\circ-35^\circ

  1. Calculate:

m∠DBC=55∘m\angle DBC=55^\circ

So, the unknown angle measures (55∘)(55^\circ).

Check: (35∘+55∘=90∘)(35^\circ+55^\circ=90^\circ), which is the measure of a right angle.

Learn by doing: Find unknown angle measures

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