Quadrilateral Interior Angles
Explore the concept of interior angles in a quadrilateral, learn how to calculate unknown angles, and understand the sum of interior angles in polygons. Discover methods to find angle values in quadrilaterals using geometry principles. Dive into visual explanations and practical examples for a comprehensive understanding.
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Presentation Transcript
23 April 2025 Angle sum in a quadrilateral LO: To calculate the value of an angle in a quadrilateral knowing the sum of the angles. www.mathssupport.org
Interior angles in polygons A quadrilateral is any shape with four straight sides On your books, use a ruler and draw a large quadrilateral similar to this one. Use a protractor to measure each of the four interior angles. Now add up the four angles. + c d b a + + What is your answer? You should find that your answer is close to 360 The sum of the interior angles of a quadrilateral is 360 . www.mathssupport.org
Interior angles in polygons The angles inside any polygon are called interior angles. b c a The sum of the interior angles of a triangle is 180 . www.mathssupport.org
Sum of the interior angles in a quadrilateral What is the sum of the interior angles in a quadrilateral? d c f a e b We can work this out by dividing the quadrilateral into two triangles. a + b + c = 180 and So, (a + b + c)+ (d + e + f )= 360 d + e + f = 180 The sum of the interior angles in a quadrilateral is 360 . www.mathssupport.org
Calculating unknown Angles Example 1 Calculate angles a and b. 76o 130o b a 88o The angles in the quadrilateral add up to 360 So, a = 360 (88 + 130 + 76 ) a = 66o The angles on a straight line add up to 180 b = 180 - 66 b = 114 So, www.mathssupport.org www.mathssupport.org
Calculating unknown Angles Example 2 Calculate the size of the four angles. a + 8o 2a + 16 a 2ao The angles in the quadrilateral add up to 360 So, we makeup an equation Simplifying + 2a +2a + 16 + a + 8 = 360 a 6a + 24 = 360 6a = 336 a = 56o 2a = 112 Substituting a 2a + 16 = 128 a + 8 = 64 www.mathssupport.org www.mathssupport.org
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