ratan19 wrote:
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
The measures of the adjacent angles of a parallelogram add up to be 180°
Given
Quote:
The ratio of the adjacent angles of a parallelogram is 7 : 8
So, 7x + 8x = 180°
Or, 15x = 180°
Or, x = 12°
Hence the angles of the parallelogram are 84° and 96°
Further it is given
Quote:
ratio of the angles of quadrilateral is 5 : 6 : 7 : 12
We know sum of all the four angles of a quadrilateral is 360°
So, 5y + 6y + 7y + 12 y = 360°
Or, 5y + 6y + 7y + 12 y = 360°
Or, 30y = 360°
Or, y = 12°
Hence the angles of the quadrilateral are 60° , 72, 84° and 144°
Quote:
sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral
Will be 84° + 84° = 168°
Hence correct answer will be (A) 168°
_________________