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Fraction Classroom · 2.3.0 · Student pages

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.

Anonymous group code: __________   Date: __________

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.

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

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

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.

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?