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.