WEBVTT
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In the figure, πΆπ· and π΅πΈ are parallel.
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Find the measure of angle π΄π΅πΈ.
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We are told in the question that the lines πΆπ· and π΅πΈ are parallel.
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Weβre asked to calculate the size of angle π΄π΅πΈ denoted by the letter π₯.
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We can see from the diagram that π΄π΅πΆπ· is a quadrilateral, a four-sided shape.
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The angles in any quadrilateral sum to 360 degrees.
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This means that the sum of the missing angle π¦, 90 degrees, 131 degrees, 69 degrees must equal 360 degrees.
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Simplifying the left-hand side gives us π¦ plus 290 is equal to 360.
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Subtracting 290 from both sides gives us π¦ is equal to 70.
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The missing angle in the quadrilateral is 70 degrees.
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We can now use the fact that cointerior or supplementary angles sum to 180 degrees.
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These are also sometimes known as C angles.
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In this question, 70 plus 69 plus π₯ must equal 180.
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This can be simplified to π₯ plus 139 is equal to 180.
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Subtracting 139 from both sides of this equation gives us π₯ is equal to 41.
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We can therefore conclude that the measure of angle π΄π΅πΈ is 41 degrees.