If shown, AB and CD are straight lines. Find x in each case.

x = 60

Step-by-step explanation:

Vertical opposite angles are formed when two straight lines intersect each other.

Given that AD and CD are two straight lines intersecting at O, the two vertical opposite formed are, ∠AOD and ∠COB. Therefore:

∠AOD = ∠COB (Vertical opposite angles are congruent)

∠AOE = 90° (right angle)

∠DOE = x

∠COF = 30°

∠BOF = 2x

m∠AOE + m∠DOE = m∠AOD (angle addition postulate)

90 + x = ∠AOD (Substitution)

m∠COF + m∠BOF = m∠COB (Angle addition postulate)

30 + 2x = ∠COB

m∠AOD = m∠COB (vertical opposite angles)

90 + x = 30 + 2x (Substitution)

Collect like terms

90 - 30 = 2x - x

60 = x

x = 60

w'x is 0.

hope it

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet