Add Non-Overlapping Adjacent Angles

Supplied materials

• Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
• Supplied worked-case record: An angle is split into adjacent turns of 28° and 47°.
• All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.

Learn the idea

Adjacent angle parts share a vertex and an inner ray. When their interiors do not overlap, their measures add to the full angle between the outside rays. Double-counting an overlapped turn would overstate the whole. A straight angle provides a useful 180-degree upper benchmark.

Identify the supplied adjacent parts and verify the stated non-overlap. Add their degree measures to find the whole. Check that the result agrees with any known right-angle or straight-angle condition.

Use the common vertex and outside rays to identify the whole. Direct addition assumes the angle interiors do not overlap. Draw three rays from one vertex and label each inner turn.

1. Draw three rays from one vertex and label each inner turn.
2. Follow the worked example. Point to each number or shape feature and say what it tells you.
3. Identify the supplied adjacent parts and verify the stated non-overlap.
4. Try the question and then the three practice questions. Check your answers and explain any change you make.

Check your reasoning

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Take it further

Adjacent 65° and 40° parts make 105°, an obtuse angle.

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