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Find unknown angles in quadrilaterals

A simple quadrilateral has interior angles whose measures sum to 360°, enabling an unknown angle to be determined by subtracting the known angle measures from 360° and representing the relationship in an equation or labeled diagram. The reasoning applies to varied orientations and to familiar quadrilateral properties, such as right angles or equal angles, without extending to formal proofs, exterior-angle generalizations, or angle sums for arbitrary polygons.

Detailed Explanation: Find unknown angles in quadrilaterals

A quadrilateral is a shape with four sides and four interior angles. The angles inside every simple quadrilateral add to:

360∘360^\circ

To find an unknown angle:

  1. Add the known angles.
  2. Subtract that total from 360∘360^\circ.
  3. Write the answer with a degree symbol.

Example

A quadrilateral has angles measuring 90∘90^\circ, 105∘105^\circ, 80∘80^\circ, and x∘x^\circ. Find xx.

First, write an equation using the angle sum:

90∘+105∘+80∘+x∘=360∘90^\circ+105^\circ+80^\circ+x^\circ=360^\circ

Add the known angles:

275∘+x∘=360∘275^\circ+x^\circ=360^\circ

Subtract 275∘275^\circ from both sides:

x∘=360∘−275∘x^\circ=360^\circ-275^\circ x=85∘x=85^\circ

The unknown angle measures 85∘85^\circ.

Learn by doing: Find unknown angles in quadrilaterals

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