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The ratio of the adjacent angles of a parallelogram is 7 : 8. Also, the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12. What is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral?
(A) 168°
(B) 228°
(C) 156°
(D) 224°
(E) None of these
(A) 168°
(B) 228°
(C) 156°
(D) 224°
(E) None of these
14 Mar 2013, 06:27
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ratan19
The ratio of the adjacent angles of a parallelogram is 7 : 8. Also, the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12. What is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral?
(A) 168°
(B) 228°
(C) 156°
(D) 224°
(E) None of these
(A) 168°
(B) 228°
(C) 156°
(D) 224°
(E) None of these
The adjacent angles of a parallelogram are supplementary (supplementary angles are two angles that add up to 180°), so we have that 7x+8x=180° --> x=12 --> the smaller angle of the parallelogram is 7x=84°.
Next, the sum of interior angles of a polygon is 180(n-2) where n is the number of sides (so is the number of angles). So, the sum of the interior angles of any quadrilateral is 180*2=360°. So, we have that 5y+6y+7y+12y=360° --> y=12° --> the second largest angle of the quadrilateral is 7y=84°.
The sum = 84°+84°=168°.
Answer: A.
For more on polygons check Polygons chapter of Math Book: math-polygons-87336.html
Also, please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Please pay attention to the rule #3. Thank you.
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