Answer:
x = 34.5
Explanation:
Did you mean to upload a different problem with a triangle? If so, just ignore my answers. If not, then my explanation will show you how to find x in the picture you provided.
Step 1: Find the measure of the angle across from the 40° angle:
- It appears that the traversal intersecting lines m and n make them parallel.
- When two straight lines intersect, they create vertical angles, which are two angles opposite each other.
- Vertical angles are always congruent and thus equal.
- The traversal intersects line m and thus the 40° angle and angle opposite it are vertical angles.
Thus, the measure of the angle opposite the 40° angle is also 40°.
Step 2: Find x by applying the Same-Side Interior Angles Theorem:
- The Same-Side Interior Angles Theorem says that when a traversal intersects two parallel lines, the same-side interior angles are supplementary and thus their sum equals 180°.
Thus, we can find x by setting the sum of the 40° we just found and the (4x + 2)° equal to 180:
40 + 4x + 2 = 180
42 + 4x = 180
4x = 138
x = 34.5
Thus, x = 34.5
When you plug in 34.5 for x, we see that the measure of the angle is 140° as 4(34.5) + 2 = 140.