Practice 1
A 90-degree angle has adjacent parts of 27 degrees and m degrees. Find m.
Answer and teaching response
63 · Subtract the known part from the whole: 90 − 27.
Find a missing part of an angle
Use a whole angle and one known part to find an adjacent missing part, with a check that the parts do not overlap.
Get the student and teacher materialsPrepare the group
Learning goal: A learner can represent angle addition with an equation and explain when the given parts make exactly the stated whole.
You will need: Paper and pencil. Use the labelled angle measures for calculation; the drawing supports the relationship rather than serving as a precision measuring instrument.
Start with this question
A 90-degree angle is split into two adjacent parts. One part measures 35 degrees. What is the other part?
55 degrees, because 35 + 55 = 90. The two parts fill the right angle with no overlap and no gap.
- Identify the two outer rays and the marked whole angle. Here the complete turn between the outer rays is 90 degrees.
- Find the interior ray that divides the whole. Confirm the parts are adjacent and meet only on that ray; overlapping parts would double-count part of the turn.
- Write 35 + m = 90, where m is the missing degree measure. Subtract the known part: m = 90 − 35 = 55.
- Check by addition. The two parts total 90 degrees, and the missing part is positive and smaller than the whole.
Run the 15-minute workshop
- 3 minutes. Trace the whole turn, then trace each part. Ask which label describes the whole.
- 4 minutes. Write and solve the missing-part equation; check that the two pieces exactly fill the outer angle.
- 5 minutes. Solve the first three items and use addition to check each result.
- 3 minutes. Use the independent check and ask what would go wrong if the two parts overlapped.
A useful error to discuss
A learner might say: Add 35 and 90 to find the missing angle.
Ninety is already the whole, not a second part. Label the outer arc as the whole and the smaller arc as the known part before choosing an operation.
Practise, then check independently
Use the first three tasks for guided practice. Try the final task without help. Record a drawing or equation as well as the answer.
Practice 2
Two non-overlapping adjacent angles measure 40 and 65 degrees. Find their combined degree measure.
Answer and teaching response
105 · The turns add because the parts join without overlap.
Practice 3
A 120-degree angle is divided into a 75-degree part and one remaining part. Find the remaining measure.
Answer and teaching response
45 · The missing part completes 75 degrees to 120 degrees.
Independent check
A straight angle measures 180 degrees. A ray divides it into adjacent parts of 125 degrees and m degrees. Find m and check by addition.
Answer and teaching response
55 · 125 + 55 = 180, so the two parts recover the straight angle.
Transfer the idea
A learner adds two angle measures from a picture without checking how their rays are arranged. Why might the sum fail to describe the marked outer angle?
Discuss a possible response
The pictured parts might overlap or leave a gap. Addition gives the marked whole only when the parts together fill it exactly once.
Choose the next teaching step
Look for:
- Labels whole and parts before calculating.
- Checks the answer using addition and the arrangement of rays.
If the idea is not secure: Colour the known and unknown arcs differently and point to the shared interior ray.
If the learner is ready: Split a 150-degree whole into three adjacent parts of 40 degrees, 65 degrees and an unknown; find the unknown 45-degree part.
Materials for your group
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