How to Understand Angles in Quadrilaterals

The interior angles of any quadrilateral total 360 degrees, which is twice a triangle because a quadrilateral splits into two triangles. That single fact lets you find any missing angle from the other three.

• Square: All angles are right angles, each measuring (90^circ).
• Rectangle: All angles are right angles, each (90^circ).
• Rhombus: Opposite angles are equal.
• Parallelogram: Opposite angles are equal; consecutive angles are supplementary (add to (180^circ)).
• Trapezoid: Angles adjacent to the parallel sides are supplementary.

Worked examples: angles in a quadrilateral

Practice questions on quadrilateral angles

1. In a rectangle, if one angle measures (85^circ), what are the measures of the other three angles?
2. In a rhombus, if one angle is (130^circ), what is the measure of its opposite angle?
3. Given a general quadrilateral with angles (A), (B), (C), and (D), if angle (A = 90^circ), angle (B = 80^circ), and angle (C = 100^circ), find angle (D).

1. In a rectangle, all angles are right angles, each measuring (90^circ). Thus, the given angle is not possible for a rectangle.
2. In a rhombus, opposite angles are equal. Thus, if one angle is (130^circ), its opposite angle is also (130^circ).
3. Angle (D = 360^circ, (90^circ + 80^circ + 100^circ) = 90^circ).

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