Question

solve for x.
(4x + 2)°
(13x - 7)°
13
work must be shown on the work paper to receive credit.
x =

Explanation:

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In a right - angled triangle, the two non - adjacent interior angles are \((4x + 2)^{\circ}\) and \(90^{\circ}\), and the exterior angle is \((13x-7)^{\circ}\). So, we can set up the equation \(4x + 2+90=13x - 7\).

Step2: Simplify the left - hand side of the equation

First, simplify \(4x + 2+90\) to \(4x+92\). The equation becomes \(4x + 92=13x-7\).

Step3: Move the \(x\) terms to one side and the constants to the other side

Subtract \(4x\) from both sides: \(92=13x - 7-4x\). Then simplify the right - hand side to get \(92 = 9x-7\).
Next, add \(7\) to both sides: \(92 + 7=9x\). So, \(99 = 9x\).

Step4: Solve for \(x\)

Divide both sides by \(9\): \(x=\frac{99}{9}\).

Answer:

\(x = 11\)