Question

enter the value of 4x + 2

Explanation:

Step1: Assume the figure is a polygon - related problem. If we assume that the exterior - angle sum property is applicable. The exterior angle of a polygon and its adjacent interior angle are supplementary. Let's assume this is a triangle - related problem (since there are three angles shown conceptually). The exterior angle at \(Q\) is \(104^{\circ}\).

Step2: Let's assume the angle at \(I\) with measure \((4x + 2)\) and the exterior - angle at \(Q\) are related by some geometric property. If we assume that the non - adjacent interior angles of a triangle are related to the exterior angle, and assume the triangle has angles \(x\), the interior angle at \(I\) (let's call it \(y\)) and the third angle. The exterior angle at \(Q\) is equal to the sum of the two non - adjacent interior angles. If we assume the other non - adjacent interior angle is \(x\) and the interior angle at \(I\) is \(y\), and we know that \(y=180-(4x + 2)\). Also, if we assume the exterior angle at \(Q\) is the sum of the non - adjacent interior angles, \(104=x+(180-(4x + 2))\).

Step3: Solve the equation \(104=x + 180-4x - 2\).

First, simplify the right - hand side: \(x+180 - 4x-2=178 - 3x\).
So, the equation becomes \(104=178 - 3x\).
Add \(3x\) to both sides: \(3x + 104=178\).
Subtract 104 from both sides: \(3x=178 - 104=74\).
Then \(x=\frac{74}{3}\).

Step4: Calculate \(4x + 2\).

Substitute \(x = \frac{74}{3}\) into \(4x+2\): \(4\times\frac{74}{3}+2=\frac{296}{3}+2=\frac{296 + 6}{3}=\frac{302}{3}\).

However, if we assume that the angle \(104^{\circ}\) and the angle \((4x + 2)\) are supplementary (a more likely assumption if this is a simple geometric figure with two angles on a straight - line or related to parallel lines etc.).

Step1: Set up the supplementary - angle equation.

Since supplementary angles add up to \(180^{\circ}\), we have \(104+(4x + 2)=180\).

Step2: Simplify the left - hand side of the equation.

\(104+4x + 2=4x+106\). So, \(4x+106 = 180\).

Step3: Solve for \(x\).

Subtract 106 from both sides: \(4x=180 - 106=74\).
Divide both sides by 4: \(x=\frac{74}{4}=\frac{37}{2}\).

Step4: Calculate \(4x + 2\).

Substitute \(x=\frac{37}{2}\) into \(4x + 2\): \(4\times\frac{37}{2}+2=74 + 2=76\).

Answer:

76