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Recognize angle addition

Angle measure is additive: when an angle is partitioned into adjacent, non-overlapping angles, the measure of the whole equals the sum of the measures of its parts, and an unknown part can be found by subtraction. This understanding applies to diagrams and whole-number degree measures, including angles forming right or straight angles; it does not extend to formal angle theorems, algebraic generalizations, or trigonometric relationships.

Detailed Explanation: Recognize angle addition

When an angle is split into smaller angles that touch side by side, the whole angle is the sum of its parts.

If one part is unknown, subtract the known part from the whole angle.

Example:
∠AOC\angle AOC is a right angle, so it measures 90∘90^\circ. Ray OB→\overrightarrow{OB} splits it into two adjacent angles. One part measures 35∘35^\circ. Find the measure of ∠BOC\angle BOC.

  1. Identify the whole angle:
∠AOC=90∘\angle AOC=90^\circ
  1. Identify the known part:
∠AOB=35∘\angle AOB=35^\circ
  1. Subtract the known part from the whole:
90∘−35∘=55∘90^\circ-35^\circ=55^\circ
  1. Write the answer:
∠BOC=55∘\boxed{\angle BOC=55^\circ}

Check: 35∘+55∘=90∘35^\circ+55^\circ=90^\circ, so the two parts make the whole right angle.

Learn by doing: Recognize angle addition

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    Angles - Remainder of 180 Degree Angle

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