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 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. So, \(x + 49=(4x - 16)+30\).

Step2: Simplify the equation

Simplify the right - hand side: \((4x - 16)+30 = 4x+14\). The equation becomes \(x + 49=4x+14\).

Step3: Solve for \(x\)

Subtract \(x\) from both sides: \(49 = 3x+14\). Then subtract 14 from both sides: \(3x=49 - 14=35\). Divide both sides by 3: \(x=\frac{35}{3}\approx11.7\).

Answer:

\(x = 11.7\)