Mathematics • Year 8 • Unit 3 • Lesson 13

Angles: Types and Naming

Build fluency with complementary (sum 90°), supplementary (sum 180°), vertically opposite (equal), and angles at a point (sum 360°). One worked example, one guided, then eight independent problems.

Build · I Do / We Do / You Do

1. I do, fully worked example

Read every line. Each step has a short reason so you see why we use 90°, 180° or 360°.

Problem. Find the complement and supplement of 37°.

Complement adds to 90°; supplement adds to 180°.

Step 1, Identify the relationship for "complement".

Complementary angles sum to 90° (C for Corner).

Reason: "complement" is what you add to make a right angle.

Step 2, Calculate the complement.

complement = 90 − 37 = 53°

Reason: subtract the given angle from 90°.

Step 3, Identify the relationship for "supplement".

Supplementary angles sum to 180° (S for Straight).

Reason: "supplement" is what you add to make a straight line.

Step 4, Calculate the supplement and check.

supplement = 180 − 37 = 143°

Check: 37 + 53 = 90 ✓ and 37 + 143 = 180 ✓.

Answer: complement = 53°; supplement = 143°.

Stuck? Revisit lesson § Card 5/6, C is for Corner (90°), S is for Straight (180°).

2. We do, fill in the missing steps

Same shape as Section 1, with the working faded. Fill in each blank. 4 marks

Problem. Find the complement and the supplement of 64°.

Step 1, Complementary angles sum to ______°:

complement = ______ − 64 = ______°

Step 2, Supplementary angles sum to ______°:

supplement = ______ − 64 = ______°

Step 3, Check complement:

64 + ______ = 90 ✓

Step 4, Check supplement:

64 + ______ = 180 ✓

Stuck? 90 − 64 = 26. 180 − 64 = 116. Both checks add back to 90 and 180 respectively.

3. You do, independent practice

Show all working and always state the rule you used. The first four are foundation (complement / supplement). The middle two are standard (vertically opposite / angles at a point). The last two are extension (ratios and reflex).

Foundation, complements and supplements

3.1 Find the complement of 45°. 1 mark

3.2 Find the complement of 23°. 1 mark

3.3 Find the supplement of 70°. 1 mark

3.4 Find the supplement of 135°. 1 mark

Standard, vertically opposite and angles at a point

3.5 Two straight lines cross. One angle is 40°. Find all four angles, and state which rule you used for each. 2 marks

3.6 Three angles meet at a point. Two of them are 90° and 120°. Find the third angle. 2 marks

Extension, ratios and reflex

3.7 Two supplementary angles are in the ratio 1 : 4. Find each angle. (Hint: 1 + 4 = 5 parts share 180°.) 2 marks

3.8 The non-reflex angle at a point is 50°. Find the reflex angle. 2 marks

Stuck on 3.7 / 3.8? Revisit lesson § Card 6 (ratios) and § Card 4 (reflex). For ratios: divide total by parts. For reflex: 360° − non-reflex.

How did this worksheet feel?

Got it Partly Lost

What I'll revisit before next class:

Answers, Do not peek before attempting

Section 2, We do (angle = 64°)

Step 1: sum to 90°, complement = 90 − 64 = 26°.
Step 2: sum to 180°, supplement = 180 − 64 = 116°.
Step 3: 64 + 26 = 90 ✓.
Step 4: 64 + 116 = 180 ✓.

3.1, Complement of 45°

90 − 45 = 45°. (45° is self-complementary.)

3.2, Complement of 23°

90 − 23 = 67°.

3.3, Supplement of 70°

180 − 70 = 110°.

3.4, Supplement of 135°

180 − 135 = 45°.

3.5, Lines crossing, one angle 40°

Vertically opposite to 40° = 40° (vert. opp. ∠s equal).
Adjacent (linear pair) = 180 − 40 = 140° (angles on a straight line).
Vertically opposite to 140° = 140° (vert. opp. ∠s equal).
All four angles: 40°, 140°, 40°, 140°. Check: 40 + 140 + 40 + 140 = 360° ✓.

3.6, Angles at a point: 90° + 120° + x

Sum at a point = 360°. So x = 360 − 90 − 120 = 150°.

3.7, Supplementary ratio 1 : 4

Total parts = 1 + 4 = 5. 1 part = 180 ÷ 5 = 36°. Angles: 36° and 144°. Check: 36 + 144 = 180 ✓.

3.8, Reflex angle if non-reflex is 50°

Reflex + non-reflex = 360°. Reflex = 360 − 50 = 310°.