A quadrilateral has two angles that measure 130° and 150°. The other two angles are in a ratio of 3:5. What are the measures of those two angles?
Question
A quadrilateral has two angles that measure 130° and 150°. The other two angles are in a ratio of 3:5. What are the measures of those two angles?
Solution
Sure, let's solve this step by step:
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First, we know that the sum of all angles in a quadrilateral is 360°.
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The sum of the two given angles is 130° + 150° = 280°.
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So, the sum of the remaining two angles is 360° - 280° = 80°.
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These two angles are in the ratio 3:5. So, we can set up the equation 3x + 5x = 80, where x is the common ratio.
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Solving for x gives us x = 80 / 8 = 10.
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Therefore, the measures of the two remaining angles are 3x = 30° and 5x = 50°.
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