Geometry

How to solve

An angle is the amount of turn between two rays that share a vertex. The diagram has no grid or protractor, so recognize the marked wedge by its shape against landmark angles — every multiple of 15° from 15° up to a near-straight 165°, the same spacing as clock-hand positions. Once you recognize it, the prompt asks for either that angle directly, its supplement (adds to 180°), or its reflex angle (adds to 360°).

Steps

  1. Identify the vertex (where the rays meet) and the marked wedge between them.
  2. Recognize the wedge's measure against the landmark angles: 15°, 30°, 45°, 60°, 75°, 90°, 105°, 120°, 135°, 150°, 165°.
  3. Answer what's asked: the angle itself, or 180° minus it (supplement), or 360° minus it (reflex).

Example

Two rays meet at O with a marked wedge recognized as a 60° angle.

  1. Asked directly: the angle is 60°.
  2. Asked for the supplement: 180° − 60° = 120°.
  3. Asked for the reflex angle: 360° − 60° = 300°.

Answer: depends on the prompt — 60, 120, or 300

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