Question

what is the value of x? x =

Explanation:

Step1: Use the exterior angle theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. In this triangle, the exterior angle is \(x\), and the two non - adjacent interior angles are both \(s - 50^{\circ}\).

Step2: Calculate the value of \(x\)

So, \(x=(s - 50^{\circ})+(s - 50^{\circ})\). But since the two sides adjacent to the angles \(s - 50^{\circ}\) are equal (as indicated by the side - length markings), we can also use the property that the exterior angle \(x\) is equal to \(2\times(s - 50^{\circ})\). Another way: If we assume the triangle is isosceles (because two sides are marked as equal), then the two base angles are equal. The exterior angle \(x\) is supplementary to the adjacent interior angle. Let's use the exterior angle formula directly. \(x = 2\times(s - 50^{\circ})\). Wait, no, actually, if we consider the basic exterior angle theorem for a triangle: \(x=(s - 50^{\circ})+(s - 50^{\circ})\). Simplifying, \(x = 2(s - 50^{\circ})\). But if we use the property of the sum of angles in a linear pair (the adjacent interior angle to \(x\) is \(180^{\circ}-x\)). And in the triangle, using the angle - sum property: \((180^{\circ}-x)+(s - 50^{\circ})+(s - 50^{\circ})=180^{\circ}\). Subtract \(180^{\circ}\) from both sides: \(-x+(s - 50^{\circ})+(s - 50^{\circ})=0\). Then \(x=(s - 50^{\circ})+(s - 50^{\circ})\). Wait, actually, if we just use the exterior angle theorem (without getting into the linear pair and triangle - angle sum, which is a longer way). The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Here, the two non - adjacent interior angles are both \(s - 50^{\circ}\). So \(x=(s - 50^{\circ})+(s - 50^{\circ})=2(s - 50^{\circ})\). But wait, no, hold on, looking at the triangle: if two sides are equal (marked as \(s\)), then the two base angles are equal. The exterior angle \(x\) is equal to the sum of the two base angles. So \(x = 100^{\circ}\) (because if we assume \(s\) is just a side - length label and not a variable for an angle, and the two non - adjacent interior angles are \(50^{\circ}\) each. Wait, no, the markings on the sides of the triangle (the two sides of the triangle that are equal) correspond to the two base angles. The exterior angle \(x\) is equal to the sum of the two base angles. If we assume that the two base angles are \(50^{\circ}\) each (because of the \(s - 50^{\circ}\) markings, and if \(s\) is a side - length, then the angles are \(50^{\circ}\) each). So \(x=50^{\circ}+50^{\circ}\)

Answer:

\(100\)