Relationship between parallelogram and quadrilateral

Question

One of the angle of a quadrilateral is twice the smallest angle of a parallelogram. The respective ratio between adjacent angle of the parallelogram is 4:5,remaining three angles is the quadrilateral are in the radio of 4:11:9 respectively. What is the Some of the smallest and greatest angle of the quadrilateral?

Answer 1

x=the smaller angle of the parallelogram

the ratio between adjacent angles is 4:5

y=the larger angle of the parallelogram

x/y=4/5

4y=5x and y=(5/4)x

x+x+(5/4)x+(5/4)x=360

4.5x=360

45x=3600

x=80º and y=100º

one angle of a quadrilateral is twice 80º or 160º

that leaves 360º-160º=200º for the sum of the remaining three angles of the quadrilateral

the three angles are in the ratio of 4:11:9

find these three angles...

4a+11a+9a=200º

24a=200º

a=200/24

a=(8 1/3)º

the angles are 4(8 1/3)=(33 1/3)º

11(8 1/3)=(91 2/3)º

9(8 1/3)=75º

the sum of the smallest and greatest angles of the quadrilateral are:

(33 1/3)º+160º=(193 1/3)º