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:
![Quadrilateral Angles - Example 1 Quadrilateral Angles - Example 1](png/quadrilateral-angles-example-1.png)
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:
![Quadrilateral Angles - Example 2 Quadrilateral Angles - Example 2](https://www.etutorworld.com/wp-content/uploads/2024/03/Quadrilateral-Angles-Example-2.png)
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
![Quadrilateral Angles - Example 3 Quadrilateral Angles - Example 3](https://www.etutorworld.com/wp-content/uploads/2024/03/Quadrilateral-Angles-Example-3.png)
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.
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