Solve for x in the problem below

x = 9

Step-by-step explanation:

This problem involves knowing the sum of angles in a triangle as well as the sum of supplementary angles. In any triangle, the sum of all the angles will always add up to 180°.  Supplementary angles add up to 180° and form a straight line.  In order to solve for 'x', we must set up an equation where the sum of the angles is equal to 180°.  Since the last angle of the triangle is not given, but we know that the value will be equal to 180 - (14x + 1), we can simplify this to 180 - 14x -1 or 179 - 14x.  We also know that this angle plus the other two angles of the triangle will add up to 180:

89 + 179 - 14x + 5x  - 7 = 180

Combine like terms:  261 - 9x = 180

Inverse operations: 261 - 261 - 9x = 180 - 261 or -9x = -81

Solve for x:  x = 9

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4