MZS = 23 , arc RS = 86

, and RU is tangent to the circle at R. Find mZU.

S

U

Step-by-step explanation:

Given

See attachment

arc

Required

Find

Let

center of the circle

We have that:

arc

This implies that:

and

is an isosceles triangle

because:

the radius of the circle

And

So, we have:

--- angles in a triangle

Collect like terms

Recall that:

So:

Divide by 2

RU is a tangent.

So:

Given that:

Considering

We have:

So:

Lastly:

Collect like terms

Hence:

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