Angles Basics

 

Basic Angle Properties

Understanding basic angle rules is essential for solving geometric problems.

Key Angle Properties:

• Angles around a point add up to $360 \degree$.

• Angles on a straight line add up to $180 \degree$.

• Vertically opposite angles are equal.

 

 

 

Worked Example: Find $x$ and $y$ in the diagram.

1.Vertically opposite angles are equal:

2. Angles on a straight line add up to 180°:

$$x + y + 98 = 180$$

$$25 + y + 98 = 180$$

$$123 + y = 180$$

 

3. Solve for $y$:

$$y = 180 -123 = 57 \degree$$

Final Answer: $x = 25 \degree$, $y = 57 \degree$

Angle Properties of Triangles

Key Triangle Properties:

• Interior angles in a triangle add up to $180 \degree$.

• Isosceles Triangle: Two angles are equal.

• Equilateral Triangle: All three angles are $60 \degree$.

• Right-Angled Triangle: Contains a $90 \degree$ angle.

 

Angle Properties of Quadrilaterals

Key Quadrilateral Properties:

• Interior angles in a quadrilateral add up to $360 \degree$.

• Squares & Rectangles: All angles are $90 \degree$.

• Parallelogram/Rhombus: Opposite angles are equal.

• Kite: One pair of opposite angles is equal.

 

Example: Find $x$ in the given quadrilateral.

 

 

Vertically opposite angles are equal:

$$A = 125 \degree$$

Angles on a straight line add up to $180 \degree$:

Interior angles in a triangle add up to $360 \degree$:

Solve for $x$:

$$x = 70 \degree$$

 

Final Answer: $x = 70 \degree$