Question

what is the value of x? write your answer as an integer or as a decimal rounded to the nearest tenth. x =

Explanation:

Step1: Apply triangle - exterior - angle theorem

The exterior - angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(41x + 48=(x + 43)+47x\).

Step2: Simplify the right - hand side of the equation

\((x + 43)+47x=x+47x + 43=48x + 43\). So the equation becomes \(41x+48 = 48x+43\).

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

Subtract \(41x\) from both sides: \(48=48x - 41x+43\), which simplifies to \(48 = 7x+43\). Then subtract 43 from both sides: \(48 - 43=7x\), so \(5 = 7x\).

Step4: Solve for \(x\)

Divide both sides by 7: \(x=\frac{5}{7}\approx0.7\).

Answer:

\(x = 0.7\)