Leopold draws a quadrilateral with two equal angles, Angles 1 and 2. Angle 3 measures 170 degrees, and Angle 4 measures either 55 degrees less than Angle 3 or 55 degrees more than Angle 3. Determine the angle measurement of Angle 2. Show all work.(
Given that Leopold draws a quadrilateral with two equal angles, let's call Angle 1 and Angle 2 as the equal angles.
Since the sum of angles in a quadrilateral is 360 degrees, we can set up an equation based on the information provided:
Angle 1 + Angle 2 + Angle 3 + Angle 4 = 360
Substitute the given values:
Angle 1 + Angle 2 + 170 + (170 ± 55) = 360
Simplify the equation based on the possible values of Angle 4:
Angle 1 + Angle 2 + 170 + (115 or 225) = 360
Now we consider the two possible cases:
Case 1: Angle 4 is 55 degrees less than Angle 3
Angle 1 + Angle 2 + 170 + 115 = 360
Angle 1 + Angle 2 + 285 = 360
Angle 1 + Angle 2 = 75
Case 2: Angle 4 is 55 degrees more than Angle 3
Angle 1 + Angle 2 + 170 + 225 = 360
Angle 1 + Angle 2 + 395 = 360
Angle 1 + Angle 2 = -35
Since angles cannot be negative, we will consider Case 1.
Now, we know that Angle 1 and Angle 2 are equal, so we can express Angle 2 in terms of Angle 1:
Angle 1 + Angle 1 = 75
2 * Angle 1 = 75
Angle 1 = 37.5 degrees
Therefore, the measurement of Angle 2 is also 37.5 degrees.