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Question
If one angle of a parallelogram is 24° less than twice the smallest angle, then the measure of the largest angle of the parallelogram is
Options
176°
68°
112°
102°
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Solution
Let the smallest angle of the parallelogram be x
Therefore, according to the given statement other angle becomes (2x - 24).
Also, the opposite angles of a parallelogram are equal.
Therefore, the four angles become x,(2x - 24) ,x and(2x - 24).
According to the angle sum property of a quadrilateral:
x +(2x - 24) + x +(2X - 24) = 360°
6x - 48° = 360°
6x - 48° = 360° + 48°
6x = 408°
`x = (408°)/6`
x = 68°
Thus, the other angle becomes
= [2(68) - 24]°
= 112°
Thus, the largest angle of the parallelogram are is 112°.
Hence the correct choice is (c).
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