Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
An angle is formed when two rays or line segments meet at a common endpoint called a vertex. The size of the angle is measured in degrees () using a tool called a protractor. Visually, you can think of an angle as the amount of 'turn' between two lines.
Acute Angles are those that measure more than but less than . Visually, these angles appear 'sharp' or narrow, similar to the tip of a pencil or a partially opened pair of scissors.
Right Angles measure exactly . These represent a perfect quarter-turn and are visualized as the 'L' shape found in the corners of a square, a book, or a room. In geometry diagrams, a right angle is uniquely marked with a small square at the vertex instead of a curved arc.
Obtuse Angles measure more than but less than . Visually, these angles look 'blunt' or wide, like the shape of a reclining beach chair or the hands of a clock showing 4:00.
Straight Angles measure exactly . A straight angle forms a perfectly flat line. Visually, it looks like a single straight line with a vertex point in the middle, representing a half-turn of a circle.
Reflex Angles are angles that measure more than but less than . Visually, they represent the 'outside' bend of an angle, similar to the angle formed on the back of your elbow when you bend your arm.
Full Rotation or Angles at a Point measure exactly . This represents a complete circle. Visually, if you start at one line and turn all the way back to the start, you have completed a turn.
Adjacent angles on a straight line always add up to . Visually, if you split a straight line into two or more parts with lines coming out of a single point, the sum of those 'inner' angles will always equal the straight angle ().
📐Formulae
💡Examples
Problem 1:
Two angles lie on a straight line. If one angle measures , calculate the value of the missing angle .
Solution:
- Identify the relationship: Angles on a straight line sum to .
- Set up the equation: .
- Subtract from both sides: .
- Calculate the result: .
Explanation:
Since the angles are supplementary (forming a straight line), we subtract the known angle from to find the unknown. The resulting angle is obtuse.
Problem 2:
An interior angle of a triangle is measured as . Calculate the reflex angle that exists on the outside of this vertex.
Solution:
- Identify the relationship: A full rotation around a point is .
- Set up the equation: .
- Subtract from both sides: .
- Calculate the result: .
Explanation:
To find a reflex angle when the interior angle is known, subtract the interior angle from a full circle (). The result is a reflex angle because it is between and .