Mathematics • Year 7 • Unit 3 • Lesson 1
Angles, Lines, and Geometry Foundations
Build fluency with classifying angles by size (acute, right, obtuse, straight, reflex) and finding unknown angles using complementary (sum 90°), supplementary (sum 180°), vertically opposite (equal) and angles at a point (sum 360°) relationships. Always state a reason.
1. I do — fully worked example
Read every line. Each step shows the geometric reason on the right — every angle answer needs one.
Problem. Two straight lines cross at a point. One of the four angles formed measures 118°. Find the other three angles and state a reason for each.
Step 1 — The vertically opposite angle.
Angle directly across the X = 118°
Reason: vert. opp. ∠s are equal.
Step 2 — An adjacent angle along the straight line.
180 − 118 = 62°
Reason: ∠s on a str. line sum to 180°.
Step 3 — The fourth angle (vertically opposite the 62°).
Fourth angle = 62°
Reason: vert. opp. ∠s are equal.
Step 4 — Check using "angles at a point".
118 + 62 + 118 + 62 = 360° ✓
Answer: The four angles are 118°, 62°, 118°, 62°.
2. We do — fill in the missing steps
Same structure as Section 1, with the working faded. Fill the blanks. 4 marks
Problem. Three angles meet at a single point. They measure 130°, 95° and x°. Find x.
Step 1 — State the rule: all angles at a single point sum to ______°.
Step 2 — Set up the equation:
130 + 95 + x = _______
Step 3 — Add the two known angles:
130 + 95 = _______
Step 4 — Solve for x:
x = 360 − _______ = _______°
Step 5 — Write the reason: ( ___________________ )
3. You do — independent practice
Show working AND a geometric reason for every answer. First four are foundation, middle two standard, last two extension.
Foundation — single step
3.1 Classify the angle 72°. 1 mark
3.2 Find the complement of 28°. 1 mark
3.3 Find the supplement of 113°. 1 mark
3.4 Two straight lines cross. One angle is 47°. State the size of the angle vertically opposite, and give the reason. 1 mark
Standard — combine two ideas
3.5 Two straight lines cross. One of the four angles is 64°. Find the other three angles. Give a reason for each. 2 marks
3.6 Four angles meet at a single point: 90°, 75°, 80° and x°. Find x. State the reason. 2 marks
Extension — push your thinking
3.7 In the angle name ∠PQR, which letter is the vertex? Then explain in one sentence why ∠PQR and ∠RQP describe the same angle. 2 marks
3.8 Two angles ∠AOB and ∠BOC sit side-by-side on a straight line AOC. ∠AOB = (2x + 10)°, ∠BOC = (3x − 5)°. Set up an equation, solve for x, and find both angles. 3 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — Three angles at a point (130°, 95°, x°)
Step 1: sum to 360°. Step 2: 130 + 95 + x = 360. Step 3: 130 + 95 = 225.
Step 4: x = 360 − 225 = 135°. Step 5: (∠s at a pt.).
3.1 — Classify 72°
72° < 90° → acute.
3.2 — Complement of 28°
Complementary angles sum to 90°. 90 − 28 = 62°.
3.3 — Supplement of 113°
Supplementary angles sum to 180°. 180 − 113 = 67°.
3.4 — Vertically opposite to 47°
47° (vert. opp. ∠s are equal).
3.5 — Four angles from a crossing (one = 64°)
Vertically opposite the 64° = 64° (vert. opp. ∠s).
Adjacent along the line = 180 − 64 = 116° (∠s on str. line).
Fourth angle = 116° (vert. opp. to the 116°).
Check: 64 + 116 + 64 + 116 = 360° ✓
3.6 — 90 + 75 + 80 + x = 360
Sum of knowns: 90 + 75 + 80 = 245. So x = 360 − 245 = 115° (∠s at a pt.).
3.7 — Vertex of ∠PQR
The middle letter is the vertex, so the vertex is Q. ∠PQR and ∠RQP describe the same angle because both have vertex Q with the same two rays (one to P and one to R) — the order you read the outside letters doesn't matter.
3.8 — (2x + 10)° + (3x − 5)° on a straight line
∠s on a str. line sum to 180°: (2x + 10) + (3x − 5) = 180.
Combine: 5x + 5 = 180. So 5x = 175 and x = 35.
∠AOB = 2(35) + 10 = 80°. ∠BOC = 3(35) − 5 = 100°.
Check: 80 + 100 = 180° ✓.