To solve this, I'm assuming that the equations both represent angles:
There is a theorem that states that an exterior angle of a triangle is equivalent to the sum of two remote triangles. Knowing this:
11x + 7 = 7x + 14 + 25
11x + 7 = 7x + 39
4x = 32
x = 8
Three hundred six thousandths . . . in word form
Our goal is to find the area
area=1/2 times base times height
we know the height is 7.9 but what is the base?
use the pythagorean theorem twice
alrighty
so
remember for legs length a and b and hytponuse c in a right triangle
a²+b²=c²
we need AD and DC
so
AD²+7.9²=9.4²
AD=√25.95
DC²+7.9²=23.2²
DC=√475.83
so
AD+DC=base=(√25.95)+(√475.83)
area=1/2bh
area=1/2((√25.95)+(√475.83))(7.9)
area≈106.28518654591426812803776879893
round to 2 decimal places
area≈106.29 square units