Question

what is the value of x?
(4x)°
(3x + 25)°
(3x + 85)°

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.
$$4x=(3x + 25)+(3x + 85)$$

Step2: Simplify the equation

First, expand the right - hand side:
$$4x=3x+25 + 3x+85$$
Combine like terms:
$$4x=6x + 110$$

Step3: Solve for \(x\)

Subtract \(6x\) from both sides:
$$4x-6x=110$$
$$-2x=110$$
Divide both sides by \(- 2\):
$$x=\frac{110}{-2}=- 55$$

But since angles cannot be negative in this context (assuming the problem is about positive - valued angles in a geometric figure), there might be a mis - interpretation. If we consider the sum of angles around a point (if the figure is a polygon - related angle problem where the sum of angles is \(360^{\circ}\)). Let's assume the sum of the three angles is \(180^{\circ}\) (if it's a triangle - like angle sum situation, but the problem is a bit unclear on the figure). Wait, re - checking the exterior angle formula application.

Wait, another approach: If we assume the sum of the three angles (if they are angles around a point or in a polygon) is \(360^{\circ}\). Let's assume the three angles \((3x + 25)+(3x + 85)+(4x)=360\)

Step1: Expand the left - hand side

$$3x+25+3x + 85+4x=360$$
Combine like terms:
$$(3x+3x + 4x)+(25 + 85)=360$$
$$10x+110=360$$

Step2: Solve for \(x\)

Subtract \(110\) from both sides:
$$10x=360 - 110$$
$$10x=250$$
Divide both sides by \(10\):
$$x = 25$$

Answer:

\(x = 25\)