In this publication, we will consider what a developed angle is, list its main properties, and also analyze an example of a task on this topic.
Determining a straight angle
Angle is deployedif its equals 180 degrees.
Those. the sides of the angle form a straight line.
Flat Corner Properties
1. A ray originating at the top of a straightened angle divides it into two angles, which are called.
- point O – the top of the corner;
- α и β – adjacent corners.
2. The bisector of a straight angle divides it into two 90° angles (i.e. ).
a = b = 90 °
3. If the ray that divides the straight angle is not its bisector, then one of the formed angles is less than 90° (acute), and the other is in the range from 90° to 180° (obtuse).
Example of a problem
Given a straight angle divided by a ray into two angles, one of which is three times the other. Find the degree measures of these angles.
Solution
Let the smaller angle be “X”, then the larger one is equal to “3x”. The sum of these angles is 180 degrees. Let’s write the corresponding equation and solve it:
x + 3x = 180
4x = 180
x = 180 : 4 = 45
So the first angle is 45° and the second is 135° (45° times 3).
Check: 45° + 135° = 180° (correct).