Straight Angle
Worked Example
Problem: Angle ABC is a straight angle. A ray BD divides it into two parts. If angle ABD measures 65°, what is the measure of angle DBC?
Step 1: A straight angle measures exactly 180°, so the two parts must add up to 180°.
∠ABD+∠DBC=180°
Step 2: Substitute the known angle and solve for the unknown.
65°+∠DBC=180°
Step 3: Subtract 65° from both sides.
∠DBC=180°−65°=115°
Answer: Angle DBC measures 115°.
Another Example
Problem: Three rays extend from point O. Ray OA and ray OC form a straight angle. Ray OB lies between them, creating angle AOB = 2x and angle BOC = 3x. Find the value of x.
Step 1: Since angle AOC is a straight angle, the two smaller angles sum to 180°.
2x+3x=180°
Step 2: Combine like terms.
5x=180°
Step 3: Divide both sides by 5.
x=36°
Answer: x = 36°, so angle AOB = 72° and angle BOC = 108°.
Frequently Asked Questions
Is a straight angle actually an angle or just a line?
It is a true angle. An angle is defined by two rays sharing a common endpoint (vertex). When those two rays point in exactly opposite directions, they form a 180° angle, which happens to look like a straight line. The geometric definition of an angle still applies.
How many radians is a straight angle?
A straight angle measures π radians. Since a full rotation is 2π radians (360°), half a rotation is π radians (180°).
Straight Angle vs. Right Angle
A straight angle measures 180° and looks like a flat line. A right angle measures 90° and forms an L-shape. A straight angle is exactly twice the size of a right angle. Two right angles placed side by side create one straight angle.
Why It Matters
Straight angles are the foundation for understanding supplementary angles — two angles are supplementary precisely when they add up to a straight angle (180°). Whenever a transversal crosses a line, the angles on one side of the intersection lie along a straight angle, which is how you derive many angle relationships in parallel-line problems. Straight angles also connect to the fact that the interior angles of a triangle sum to 180°.
Common Mistakes
Mistake: Confusing a straight angle (180°) with a full rotation (360°).
Correction: A straight angle is a half-turn, not a full turn. A full rotation is 360°, which brings a ray all the way back to its starting position. A straight angle only sends the ray to the opposite direction.
Mistake: Thinking a straight angle is not a real angle because it looks like a line.
Correction: An angle is defined by two rays sharing a vertex. At 180° the rays happen to be collinear, but the angle still exists. Similarly, a 0° angle (two overlapping rays) is also a valid angle.
Related Terms
- Angle — General term; straight angle is a specific case
- Right Angle — A 90° angle, half of a straight angle
- Supplementary Angles — Two angles that together form a straight angle
- Degree — Unit of angle measurement
- Reflex Angle — An angle greater than 180° but less than 360°
- Obtuse Angle — An angle between 90° and 180°
- Linear Pair — Adjacent angles that form a straight angle