Quadrilateral Hierarchy Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
A quadrilateral has three angles of 85°85°, 95°95°, and 110°110°. Find the fourth angle.

Solution

  1. 1
    Step 1: Recall that the sum of interior angles of any quadrilateral is 360°360°.
  2. 2
    Step 2: Let the fourth angle be xx. Then 85+95+110+x=36085 + 95 + 110 + x = 360.
  3. 3
    Step 3: 290+x=360290 + x = 360, so x=70°x = 70°.

Answer

The fourth angle is 70°70°.
The interior angles of any quadrilateral (4-sided polygon) sum to 360°. This can be shown by dividing any quadrilateral into two triangles with a diagonal — each triangle contributes 180°, for a total of 360°. This fact applies to all quadrilaterals: squares, rectangles, parallelograms, trapezoids, and irregular quadrilaterals.

About Quadrilateral Hierarchy

The quadrilateral hierarchy organizes four-sided polygons by their properties in a classification tree. Every square is a rectangle, every rectangle is a parallelogram, and every parallelogram is a trapezoid — each level adds constraints like equal sides or right angles.

Learn more about Quadrilateral Hierarchy →

More Quadrilateral Hierarchy Examples

Example 2 medium

Explain the quadrilateral hierarchy: How is a square related to a rectangle, rhombus, and parallelog

Example 3 easy

A quadrilateral has all angles equal. What type of quadrilateral is it? What is each angle's measure

Example 4 hard

In parallelogram [formula], [formula] and [formula]. Find all four angles. Use the property that con

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