Angles on a Straight Line

Learn that angles on a straight line always add up to 180°

Understanding Angles on a Straight Line

When two or more angles meet at one point on a straight line, on the same side of the line, they add up to 180°. This is because a straight line is half of a full turn (360° ÷ 2 = 180°).

Key Rule:

Sum of angles on a straight line = 180°

Example 1: Two Angles on a Straight Line

a + b = 180°

Angles on a straight line sum to 180°

The angles are on a straight line.

$\angle a + \angle b = 110° + 70° = 180°$

Example 2: Three Angles on a Straight Line

p + q + r = 180°

Angles on a straight line sum to 180°

The angles are on a straight line.

$\angle p + \angle q + \angle r = 65° + 58° + 57° = 180°$

Finding Unknown Angles (Two Angles)

When you know one angle on a straight line, you can find the other by subtracting from 180°.

Worked Example: Find the unknown angle

The angles are on a straight line. Find ∠x.

Solution:

Angles on a straight line sum to 180°

$\angle x = 180° - 125° = 55°$

Finding Unknown Angles (Three or More Angles)

When there are multiple angles, add all the known angles first, then subtract from 180°.

Worked Example: Three angles on a line

The angles are on a straight line. Find ∠c.

Solution:

First, add the known angles: $33° + 46° = 79°$

Then subtract from 180°:

$\angle c = 180° - 79° = 101°$

Practice Problems

Practice 1: Find angle k

The angles are on a straight line. Find ∠k.

ShowHide solution

$15° + 144° = 159°$

$\angle k = 180° - 159° = 21°$

Practice 2: Find angle m

The angles are on a straight line. Find ∠m.

ShowHide solution

$\angle m = 180° - 67° = 113°$

Practice 3: Find angle n

The angles are on a straight line. Find ∠n.

ShowHide solution

$52° + 73° = 125°$

$\angle n = 180° - 125° = 55°$

Key Takeaways

Angles on a straight line that meet at one point add up to 180°
A straight line is half of a full turn (360° ÷ 2 = 180°)
To find an unknown angle: subtract the known angles from 180°
This rule works for 2, 3, or more angles on a line