Question

find x.
124° 41° 44° x°
your answer
x =

Explanation:

Step1: Find the adjacent angle of \(124^{\circ}\)

The adjacent angle of \(124^{\circ}\) is \(180 - 124=56^{\circ}\) (supplementary angles sum to \(180^{\circ}\)).

Step2: Use the exterior - angle property of a triangle

The exterior - angle property of a triangle states that the exterior angle is equal to the sum of the two non - adjacent interior angles.
Let's assume the triangle. The exterior angle \(x\) is related to the angles inside the triangle.
We know that \(x=56 + 41+44 - 180+180\) (using the angle sum property of a triangle and exterior - angle relations).
Another way:
The sum of angles around a point on a straight line and using triangle angle properties.
First, the angle adjacent to \(124^{\circ}\) is \(a = 180^{\circ}-124^{\circ}=56^{\circ}\)
The sum of angles in a triangle - like structure (using the fact that the sum of angles around a point and triangle angle sum)
\(x=56^{\circ}+41^{\circ}+44^{\circ}- 180^{\circ}+180^{\circ}\) (more simply, using the exterior - angle theorem in a generalized sense for the figure)
\(x = 56+41 + 44-180 + 180\) (a better approach: consider the angles in the figure. The sum of the non - \(x\) angles related to the line:
The angle adjacent to \(124^{\circ}\) is \(56^{\circ}\). Then, using the fact that the sum of angles in the "angle chain" (considering the straight line \(180^{\circ}\))
\(x=56 + 41+44-180 + 180\) (a more straightforward way:
We know that the sum of angles on a straight line is \(180^{\circ}\). Let's consider the angles formed by the intersecting lines.
The angle adjacent to \(124^{\circ}\) is \(180 - 124=56^{\circ}\)
Now, using the property that the sum of angles in the "angle group" related to \(x\):
\(x=56+41 + 44\) (by the exterior - angle theorem for a polygon - like angle relation in this figure)
\(x=141^{\circ}\)

Answer:

\(x = 141\)