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Calculate the size of angles 𝑎 and 𝑏 in this diagram.
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We need to calculate the size of these two angles, 𝑎 and 𝑏.
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This shape is a quadrilateral; it has four sides.
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The angles in a quadrilateral add up to 360 degrees.
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This angle is a right angle.
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So we know it measures 90 degrees.
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So this angle also measures 90 degrees.
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Angle 𝑎 is equal to its opposite angle, which is 160 degrees.
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Now, we just need to calculate how much angle 𝑏 measures.
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We already have the measurements for the other three angles, 90 plus 90 plus 160.
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90 and 90 is 180.
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180 add 160 is 340.
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We know that the angles in a quadrilateral total 360 degrees.
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So we can subtract the sum of the other three angles from 360.
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360 subtract 340 equals 20.
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So angle 𝑏 measures 20 degrees.
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Angle 𝑎 is 160 degrees and angle 𝑏 is 20 degrees.