Straight Angle

The angle formed on a point on a line segment is called a straight angle. Whenever two-line rays meet at a point, the angle formed at the intersection is 180 degrees.

The angle formed at these intersections of lines is called a supplementary angle or a flat angle. In mathematics, a straight angle means a vertex point of an angle whose value is 180 degrees.

The vertex is a common point where two arms of an angle meet. The angle formed on a straight line is always equal to 180 degrees. That is what a straight angle means.

Facts about a straight angle

1. 180 degrees in radians is denoted by pi (π).
2. At times, 180 degrees is referred as supplementary.
3. A human’s line of sight is a perfect example of a straight angle.

Practical examples of a straight angle

1. The angle formed by a protractor is 180 degrees.
2. The angle formed by the hour and minute hand when it strikes 6.
3. The angle formed on the surface of water when it is stagnant.

Properties of a straight angle

1. Half of a revolution forms a straight angle.
2. It can be formed by joining two right angles.
3. The rays forming a straight angle will show opposite directions.
4. In order to form a 180 degree, one of the rays has to turn in the opposite direction forming a semi-circle. A practical example can be seen at the turnaround on the roads.
5. The straight angle is measure positive when measured clockwise and negatively when measured anti-clockwise.

Find the straight angle pairs. Also, if angle 1 is 50 degrees, find the other angles.

Solution
Part 1 –
The lines AC and DB are straight.
Therefore, the angles formed on these lines will be equal to 180 degrees.
∠1 and ∠4, ∠3 and ∠4, ∠3 and ∠2, ∠2 and ∠1 are the pairs of straight angles.


Part 2 –
∠1 = 50°
We know, the angle formed on a straight line is equal to 180°.
Therefore, ∠1+∠4 = 180°
50° + ∠4 = 180°
∠4 = 130°
Also, opposite angles on a straight angle are equal.
This implies, ∠3=∠1=50°
∠2=∠4=130°

Check – The sum of all the angles at a point must be equal to 360°.
This implies ∠1+∠2+∠3+∠4=360°
Therefore, 50°+130°+50°+130°=360°
Hence, proved.

How to draw a straight angle from a protractor?

1. Draw a line segment OA.
2. Place the protractor on point O, coinciding with the line segment OA.
3. Mark 180 degree and 0 degree on the paper with the help of the protractor.
4. Join the point of 180 degree and OA line segment to form a straight angle.
5. Make sure to mark an arrowhead showing 180 degrees on point O after making the straight angle.

Fun fact: - We cannot consider a straight angle as a triangle. Even though the sum of all angles inside a triangle equals 180 degrees, we cannot consider a triangle a straight angle. Why? Because the straight angle is not an enclosed figure. A triangle is an enclosed figure, whereas a straight angle is not. Therefore, a straight angle cannot be considered a triangle.