How to Understand Angles in Quadrilaterals

• 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.

Examples

Practice Questions:

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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