Quadrilateral Angles

Grade 7 Math Worksheets

A quadrilateral is a polygon with four edges (or sides) and four vertices (or corners). The sum of the interior angles in any quadrilateral is always 360 degrees.

Let’s denote the four angles of a quadrilateral as A, B, C, and D. The sum of these angles is always 360 degrees, represented as

A + B + C + D = 360 degrees

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Quadrilateral Angles - Grade 7 Math Worksheet PDF

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Depending on the properties of the quadrilateral, the angles may have different relationships. Here are some common types of quadrilaterals and their angle properties:

Rectangle: In a rectangle, opposite sides are equal and each angle measures 90 degrees.

Square: A square is a special case of a rectangle where all four sides and four angles are equal. Each angle measures 90 degrees.

Parallelogram: Opposite angles in a parallelogram are equal. Adjacent angles add up to 180 degrees.

Trapezoid: The sum of the two adjacent angles in a trapezoid is 180 degrees.

Rhombus: In a rhombus, all sides are equal, and opposite angles are equal

Kite: In a kite, the angles between the two pairs of adjacent sides are equal.

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Example Questions

1. Find Angles L, K, M, and M in the parallelogram given below:

The quadrilateral is a parallelogram.

So Opposite angles are equal and adjacent angles are supplementary

∠L = ∠N = 67 Degrees (Opposite angles of a parallelogram)

∠K = 180 – ∠N = 180 – 67 = 113 Degrees

∠M = ∠K = 113 Degrees (Opposite angles of a parallelogram)

2. Find angles A, B, C and D in the parallelogram given below:

Solution

The quadrilateral is a parallelogram.

So Opposite angles are equal and adjacent angles are supplementary

∠B = ∠D = x = 120 degrees (Opposite angles of a parallelogram)

∠C = ∠A = z = y = 180 – ∠B = 180 – 120 = 60 degrees

∠A = 60 degrees

∠B = 120 degrees

∠C = 60 degrees

∠D = 120 degrees

3. Find angles A, B, C and D

Solution

The quadrilateral is a Trapezoid and adjacent angles add up to 180o

So 2x + 10 + x + 20 = 180 degrees

=> 3x + 30 = 180 degrees

=> 3x = 150 degrees

=> x = 50 degrees

∠A = 2x + 10 = 2(50) + 10 = 110 degrees

∠D = x + 20 = 50 + 20 = 70 degrees

∠C = 92 degrees

∠C + ∠B = 92 + ∠B = 180 degrees

=> ∠B = 180 – 92 = 88 degrees

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Quadrilateral Angles FAQS

What is the sum of the interior angles of a quadrilateral?

The sum of the interior angles of any quadrilateral is always 360 degrees.

Are all angles in a quadrilateral always equal?

No, not all angles in a quadrilateral are necessarily equal. The angles can vary depending on the type of quadrilateral.

What are the angles of a rectangle?

In a rectangle, opposite angles are equal, each measuring 90 degrees

What are the angles of a square?

A square is a special type of rectangle where all four angles are equal, each measuring 90 degrees.

What are the angles of a parallelogram?

In a parallelogram, opposite angles are equal.

What is the sum of the adjacent angles in a trapezoid?

The sum of the two adjacent angles in a trapezoid is always 180 degrees.

Are all angles in a rhombus equal?

No, all angles in a rhombus are not necessarily equal, although opposite angles are equal.

What are the angles of a kite?

In a kite, the angles between the two pairs of adjacent sides are equal.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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