Geometry: Equations, Angles and Area
A free maths worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.
Geometry: Equations, Angles and Area
Reference and angle equations
Learning focus: AC9M7M01, AC9M7M04, AC9M7M05, AC9M8M01 and AC9M8SP01.
Instructions: Write an equation before solving. Show all working and give a reason for angle answers. Add a diagram where it helps.
Formula reference
Angles on a straight line: a + b = 180°
Angles around a point: sum = 360°
Vertically opposite angles are equal.
Triangle angle sum: a + b + c = 180°
Polygon interior angle sum: (n − 2) × 180°
Rectangle: A = lw and P = 2l + 2w
Triangle: A = ½bh
Parallelogram: A = bh
Similarity: k = image length ÷ original length; image length = k × original length; area scale factor = k²
Triangle, polygon, area and similarity problems
Answer key
1. Equation: x = 68°. Answer: x = 68°. Reason: corresponding angles on parallel lines are equal.
2. Equation: (3x + 20) + (2x + 10) = 180; 5x + 30 = 180; x = 30. Angles: 110° and 70°.
3. Equation: 4x + 8 = 6x − 32; 40 = 2x; x = 20. Angle: 88°. Reason: vertically opposite angles are equal.
4. Equation: 3x + 15 = 5x − 25; 40 = 2x; x = 20. Angle: 75°. Reason: alternate interior angles on parallel lines are equal.
5. Equation: 52 + 67 + x = 180. Therefore x = 61°.
6. Equation: 44 + x + x = 180; 2x = 136; x = 68°. Each base angle is 68°.
7. Equation: 90 + 110 + 85 + x = 360. Therefore x = 75°.
8. Sum = (6 − 2) × 180 = 720°. Each angle = 720 ÷ 6 = 120°.
9. Area: A = 8.5 × 4 = 34 m². Perimeter: P = 2(8.5) + 2(4) = 25 m.
10. A = ½ × 12 × 7 = 42 cm².
11. A = 9.2 × 5 = 46 m².
12. Area = 10 × 8 − 4 × 3 = 80 − 12 = 68 m². Perimeter = 10 + 8 + 6 + 3 + 4 + 5 = 36 m.
13. Enlarged length = 1.5 × 8 = 12 km.
14. Yes. The triangles are congruent by SSS because all three corresponding side lengths are equal.
15. Equation: ((n − 2) × 180) ÷ n = 150. Thus 180n − 360 = 150n, so 30n = 360 and n = 12. Perimeter = 12 × 3.5 = 42 m.
About This Worksheet
Free in Kuraplan
Sign up free, grab the PDF, and customize it for your class.
Print-Ready
Formatted for standard paper. Clean layout, easy to read.
AI-Generated
Created with Kuraplan's AI, designed for real classroom use.
For Teachers & Parents
Use in classrooms, for homework, tutoring, or homeschool.
Need a custom version of this worksheet?
Kuraplan's AI generates custom worksheets in seconds — differentiated for every learner, aligned to your curriculum.
Generate Custom Worksheets — Free
