We are asked to find the value of x. Notice that the x^(∘) angle is one of the exterior angles of the polygon in the diagram. To find the measure of the x^(∘) angle, we will first recall an important piece of information.
This means that the sum of the exterior angles of the given triangle is also 360^(∘). Let's mark an exterior angle at each vertex of this triangle.
The exterior angles of the triangle have measures of x^(∘), 150^(∘), and y^(∘). These measures add up to 360^(∘).
x^(∘) + 150^(∘) + y^(∘) = 360^(∘)
We can use this equation to find the value of x, but we need to find the value of y first. Notice that the y^(∘) angle and the 100^(∘) angle form a straight line.
Therefore, these angles are supplementary and the sum of their measures is 180^(∘).
y^(∘) + 100^(∘) = 180^(∘)
Now we can solve this equation for y. For simplicity, we will not write the degree symbol.
