Question

what is the value of x?
x =

Explanation:

Step1: Identify the angle relationship

The angle \((3x + 85)^\circ\) is an exterior angle of the triangle, so it is equal to the sum of the two non - adjacent interior angles \((4x)^\circ\) and \((3x + 25)^\circ\). So we can write the equation: \(3x + 85=4x+(3x + 25)\)

Step2: Simplify the right - hand side of the equation

Simplify \(4x+(3x + 25)\) to get \(4x + 3x+25=7x + 25\). So the equation becomes \(3x + 85=7x + 25\)

Step3: Solve for \(x\)

Subtract \(3x\) from both sides: \(85=7x - 3x+25\), which simplifies to \(85 = 4x+25\)
Subtract 25 from both sides: \(85 - 25=4x\), so \(60 = 4x\)
Divide both sides by 4: \(x=\frac{60}{4}=15\)

Answer:

\(x = 15\)