Right Angles and Angles on a Straight Line

This page introduces two fundamental angle concepts in geometry: right angles and angles on a straight line.

Right Angles

The guide begins by explaining that angles that add up to 90 degrees are called right angles. It provides a visual representation of a right angle and states that the angles within a right angle always sum to 90°.

Definition: A right angle is an angle that measures exactly 90 degrees.

An example is given to illustrate how to calculate a missing angle in a right angle:

Example: If one angle in a right angle is 60°, the other angle can be calculated by subtracting 60° from 90°, resulting in 30°.

Angles on a Straight Line

The page then moves on to explain the concept of angles on a straight line.

Highlight: Angles on a straight line add up to 180 degrees.

This principle is illustrated with a diagram showing a straight line divided into three angles.

Example: In a problem where two angles on a straight line are given (55° and 120°), the third angle can be calculated by subtracting the sum of the known angles from 180°: 180° - (55° + 120°) = 5°.

The guide provides several examples of calculating missing angles on a straight line, reinforcing the concept that the sum must always equal 180°.

Angles at a Point

This page focuses on the concept of angles at a point and provides practical examples for calculating missing angles.

Definition: Angles at a point always add up to 360 degrees.

The page presents three different scenarios involving angles at a point, each with a diagram and step-by-step solution.

Example 1: A diagram shows five angles at a point, with four known angles (160°, 105°, 45°, and 95°) and one unknown angle x. The solution demonstrates how to find x by subtracting the sum of the known angles from 360°.

Example: 360° - (160° + 105° + 45° + 95°) = 360° - 405° = -45°

Since a negative angle is not possible in this context, the answer is adjusted to 360° - 45° = 315°.

Example 2: Another diagram shows three angles at a point, with two known angles (95° and 140°) and one unknown angle x. The solution shows a simpler calculation:

Example: x = 360° - (95° + 140°) = 360° - 235° = 125°

Example 3: The final example presents four angles at a point, with three known angles (95°, 45°, and 80°) and one unknown angle x. The solution follows the same principle:

Example: x = 360° - (95° + 45° + 80°) = 360° - 220° = 140°

These examples reinforce the concept of angles at a point calculations and provide students with practice in applying the principle that angles at a point sum to 360°.

Highlight: The page emphasizes the importance of checking that the sum of all angles at a point equals 360° to verify the correctness of calculations.