Question

The tower shown is supported by parallel guy wires such that m<1 = (2x +20)° and m<2 = (4x-6)° Government regulations stale the angle the wire forms with the ground cannot exceed 45°. Does the angle of the guy wire fall within government regulation

Answer 1

The wires are parallel lines. If you consider the floor to be a perpedicular line that crosses both parallel lines. Then angles m∠1 and m∠2 are corresponding angles (the lines form an F shaped line), this means, that they are equal, so:

m∠1=m∠2

If you replace ir with the given expressions you will determine a one unknown equation:

$2x+20=4x-6$

Solve for x

$\begin{gathered} 2x-4x=-6-20 \\ -2x=-26 \\ x=13 \end{gathered}$

Using the value of x replace in the formulas to determine the measure of the angles

m∠1=2x+20=2*13+20=46º

m∠2=4x-6=4*13-6=46º

The angle og the guy wires are off the goverment regulations by one degree.