1. Given that the first angle is three-fourth of the fourth angle, second angle is one-fourth of the fourth angle and third angle is half of the fourth angle of a quadrilateral. If the sum of all the interior angles of a quadrilateral is 360°, find all its interior angles.
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Given that the first angle is three-fourth of the fourth angle, second angle is one-fourth of the fourth angle and third angle is half of the fourth angle of a quadrilateral. If the sum of all the interior angles of a quadrilateral is 360°, find all its interior angles
Let the measure of the fourth angle be x°.
We know that the sum of the angles of a quadrilateral is 360°.
Therefore, 54 + 80 + 116 + x = 360
⇒ 250 + x = 360
⇒ x = (360 - 250) = 110.
Hence, the measure of the fourth angle is 110°.
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