In ΔSTU, \overline{SU} SU is extended through point U to point V, \text{m}\angle STU = (2x+8)^{\circ}m∠STU=(2x+8) ∘ , \text{m}\angle TUV = (7x-5)^{\circ}m∠TUV=(7x−5) ∘ , and \text{m}\angle UST = (x+19)^{\circ}m∠UST=(x+19) ∘ . What is the value of x?X?

The value of x is 8

Step-by-step explanation:

Refer the attached figure

is an exterior angle

Exterior angle property : The sum of the two opposite interior angles is equal to the exterior angle

So,

Hence the value of x is 8

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2