Question - Finding Angle Measurements on Intersecting Lines
Solution:
The image shows two lines intersecting, with one line labeled "m" and the other line unlabeled. At the intersection, there are two angles marked: one is 56 degrees, and the other has an angle marking but no degree written. Additionally, the angle between line "m" and the vertical line on the left is labeled with an angle mark and "x," indicating the measure of this angle is unknown. Also, "y" is marked at the angle between the vertical line and the horizontal line on the bottom. We need to find the values of x and y.Here is how you can find the values of x and y:1. Since the lines are forming a straight line at both the points where x and y are marked (which are on a straight line), we know that the sum of angles on a straight line is 180 degrees.2. Let's find x first. We are given a part of angle x (56 degrees), which means we need to subtract that from 180 degrees to find the remainder of angle x: $$ x = 180^\circ - 56^\circ = 124^\circ $$ So, angle x = 124 degrees.3. Now, let's find y. We do not have a direct measurement but we do know that line "m" is a straight line. Since x is 124 degrees, the angle adjacent to x on the other side of line "m" must also be 124 degrees (because they are vertically opposite angles, which are equal).4. Now, to find angle y, since it is on a straight line with the 124-degree angle, we subtract 124 degrees from 180 degrees: $$ y = 180^\circ - 124^\circ = 56^\circ $$ So, angle y = 56 degrees.In conclusion, x = 124 degrees and y = 56 degrees.
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