Grade 8 - Space & Shape: Angles and Geometry Worksheet

Instructions: State the geometric property you use for each step. Show all calculations clearly. Include units (degrees) in every answer.

Section A: Classifying Angles (5 marks)

Classify each angle as acute, right, obtuse, straight, reflex or revolution:

1. $47°$ (1)
2. $90°$ (1)
3. $135°$ (1)
4. $180°$ (1)
5. $210°$ (1)

Section B: Angle Relationships (6 marks)

1. Two angles are supplementary. One angle is $3x + 10°$ and the other is $2x - 5°$. Find the value of $x$ and both angles. (3)

2. Two angles are vertically opposite. One angle is $4x - 20°$ and the other is $2x + 40°$. Find $x$ and the size of both angles. (3)

Section C: Triangles (5 marks)

1. Can a triangle have angles $60°$, $80°$ and $50°$? Show your reasoning. (2)

2. An isosceles triangle has one angle of $40°$. Find the sizes of the other two angles. Show ALL possible solutions. (3)

Section D: Quadrilaterals (4 marks)

In a rhombus, one angle is $65°$. Find the sizes of all four angles. Give a reason for each answer.

Total: 20 marks