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Fraction Classroom · 2.3.0 · Teacher answers & responses

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.

The interior ray splits the 90° whole into a known 35° part and one unknown adjacent part.35°?90° whole
The interior ray splits the 90° whole into a known 35° part and one unknown adjacent part.

Build the idea

model. A 90-degree angle is split into two adjacent parts. One part measures 35 degrees. What is the other part?

  1. Identify the two outer rays and the marked whole angle. Here the complete turn between the outer rays is 90 degrees.
  2. 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.
  3. Write 35 + m = 90, where m is the missing degree measure. Subtract the known part: m = 90 − 35 = 55.
  4. Check by addition. The two parts total 90 degrees, and the missing part is positive and smaller than the whole.

Worked example: 55 degrees, because 35 + 55 = 90. The two parts fill the right angle with no overlap and no gap.

Practise and explain

Try p1–p3 with a partner. Use a drawing and label your units. Try e1 independently before comparing responses.

p1. A 90-degree angle has adjacent parts of 27 degrees and m degrees. Find m.

Answer: 63

Teacher response: Subtract the known part from the whole: 90 − 27.

p2. Two non-overlapping adjacent angles measure 40 and 65 degrees. Find their combined degree measure.

Answer: 105

Teacher response: The turns add because the parts join without overlap.

p3. A 120-degree angle is divided into a 75-degree part and one remaining part. Find the remaining measure.

Answer: 45

Teacher response: The missing part completes 75 degrees to 120 degrees.

e1. 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: 55

Look for:

  • Labels whole and parts before calculating.
  • Checks the answer using addition and the arrangement of rays.

Teacher response: 125 + 55 = 180, so the two parts recover the straight angle.

Transfer the idea

transfer. 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?

Answer: The pictured parts might overlap or leave a gap. Addition gives the marked whole only when the parts together fill it exactly once.

Run the 15-minute workshop

teach-1. 3 minutes: Trace the whole turn, then trace each part. Ask which label describes the whole.

teach-2. 4 minutes: Write and solve the missing-part equation; check that the two pieces exactly fill the outer angle.

teach-3. 5 minutes: Solve the first three items and use addition to check each result.

teach-4. 3 minutes: Use the independent check and ask what would go wrong if the two parts overlapped.

Respond to the learner

misconception. Add 35 and 90 to find the missing angle.

Teacher response: 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.

support. Colour the known and unknown arcs differently and point to the shared interior ray.

extend. Split a 150-degree whole into three adjacent parts of 40 degrees, 65 degrees and an unknown; find the unknown 45-degree part.

Teaching notes