If o n = 8 x − 8 , l m = 7 x + 4 , n m = x − 5 , and o l = 3 y − 6 , find the values of x and y for which lmno must be a parallelogram

x=12 and y=4.3

Step-by-step explanation:

Given the sides of quadrilateral that are  O N = 8 x − 8 , L M = 7 x + 4 , N M = x − 5 , and O L = 3 y − 6. we have to find the value of x and y so that LMNO  be a parallelogram.

we know opposite sides of parallelogram are equal.

Hence, we have to find the value of x and y such that opposite sides becomes equal which implies LMNO is a parallelogram.

Equating opposite sides equal, we get

8x-8=7x+4 ⇒ 8x-7x=8+4=12 ⇒ x=12

implies, NM=x-5=12-5=7

NM=OL ⇒ 3y-6=7 ⇒ 3y=13 ⇒ y=4.3

Hence, x=12 and y=4.3

d. it is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.

step-by-step explanation: