Problema Solution
a quadrilateral is a polygon with 4 sides. the sum of the measures of the 4 angles in a quadrilateral is 360 degrees. if the measures of the angles of quadrilateral are consecutive odd integers, find the answers
Answer provided by our tutors
let the consecutive odd integers that represent the measures of the angles be:
2x-3, 2x - 1, 2x + 1, 2x + 3, where x is integer
the sum of the measures of the 4 angles in a quadrilateral is 360 degrees:
2x - 3 + 2x - 1 + 2x + 1 + 2x + 3 = 360
by solving we find
x = 45
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2x - 3 = 2*45 - 3 = 87 degrees
2x - 1 = 89 degrees
2x + 1 = 91 degrees
2x + 3 = 93 degrees
Indeed 87 + 89 + 91 + 9 3 = 360.
The measures of the angles of quadrilateral are 87, 89, 91 and 93 degrees.