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Find unknown angles on a straight line

Adjacent angles whose noncommon sides form a straight line are supplementary, so their measures total 180°; an unknown angle can be determined by subtracting known angle measures from 180°, including diagrams with more than two adjacent angles. The angles need not be equal, and this scope does not include formal algebraic generalizations or broader angle relationships such as angles around a point or parallel-line theorems.

Detailed Explanation: Find unknown angles on a straight line

When adjacent angles lie on a straight line, their measures add up to 180∘180^\circ.

Example

In the diagram, three adjacent angles form a straight line:

        47°   x°   68°
─────────╱────╱────╱────────

Find xx.

  1. Since the angles form a straight line, their total is 180∘180^\circ:

47∘+x+68∘=180∘47^\circ+x+68^\circ=180^\circ

  1. Add the known angles:

47∘+68∘=115∘47^\circ+68^\circ=115^\circ

  1. Subtract the known total from 180∘180^\circ:

x=180∘−115∘x=180^\circ-115^\circ

  1. Calculate:

x=65∘x=65^\circ

So, the unknown angle is 65∘\boxed{65^\circ}. Check: 47∘+65∘+68∘=180∘47^\circ+65^\circ+68^\circ=180^\circ.

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