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Quadrilaterals angle sum property a

Before talking about the quadrilaterals angle sum property, let us recall what angles and
quadrilateral is
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An angle
is measured in degrees (°)
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The quadrilateral is four-sided polygon which can have or not have equal
sides
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A quadrilateral is a
polygon which has 4 vertices and 4 sides enclosing 4 angles and the sum of all the angles is
360°
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Both
these triangles have an angle sum of 180°
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Angle sum is one of the properties of quadrilaterals
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Angle Sum Property of a Quadrilateral
According to the angle sum property of a Quadrilateral, the sum of all the four interior angles is 360 degrees
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AC is a diagonal
AC divides the quadrilateral into two triangles, ∆ABC and ∆ADC

We have learned that the sum of internal angles of a quadrilateral is 360°, that is, ∠ABC + ∠BCD + ∠CDA +
∠DAB = 360°
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

We know that the sum of angles in a triangle is 180°
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

Replacing them we have,

∠D + ∠DAB + ∠BCD + ∠B = 360°


That is,

∠D + ∠A + ∠C + ∠B = 360°
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This is the angle sum property of quadrilaterals
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The sum of its interior angles is 360 degrees
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In the image given below, a Trapezoid (also a type of Quadrilateral) is shown
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Hence,
∠A = ∠B = ∠C = ∠D = 90°

A quadrilateral, in general, has sides of different lengths and angles of different measures
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are special types of quadrilaterals with some of their
sides and angles being equal
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To prove this, the scalene trapezium has the side length of different measure,
which does not have opposite angles of 180 degrees
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It means that the angles add up to 180 degrees
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It means that the sum of the quadrilateral
angles is equal to 360 degrees, but it is not necessary that the opposite angles in the
quadrilateral should be of 180 degrees
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They are;
1
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2
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3
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4
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5
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Example
1
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Solution: By the angle sum property we know;
Sum of all the interior angles of a quadrilateral = 360°
Let the unknown angle be x
So,
90° + 45° + 60° + x = 360°
195° + x = 360°
x = 360° – 195°
x = 165°



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