The sum of the measures of the interior angles of a convex n-gon is (n-2)*180^(∘).
In this case, expressions are given for the measures of the interior angles. We can write an equation where the sum of these expressions is equal to (n-2)180.
116^(∘) + 3x+8^(∘) + 32^(∘) + 2x-1^(∘)= (n-2)180
Our polygon has 4 sides, so we can substitute 4 for n.
116^(∘) + 3x+8^(∘) + 32^(∘) + 2x-1^(∘) = (4-2)180^(∘)
Finally, let's solve the equation above for x.
If a transversal intersects two parallel lines, then corresponding angles are congruent.
We can visualize this theorem. Consider two lines l and m, where l∥ m.
This allows us to find the measure of one of the angles with which the leftmost one forms a linear pair.
The measures of angles forming a linear pair must sum to 180^(∘). This allows us to write the following equation.
7x-3^(∘) + 4x+12^(∘) = 180^(∘)
Let's solve this equation for x.
