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

Answer 1

Let x be the measure of angle 4.

Since angles 1 and 2 are equal, let's call them both y.

From the given information, we know that:
Angle 1 = Angle 2 = y
Angle 3 = 170 degrees
Angle 4 = x

We also know that either
x = 170 - 55 = 115 degrees
or
x = 170 + 55 = 225 degrees

Since angles in a quadrilateral add up to 360 degrees, we can write the equation:
y + y + 170 + x = 360
2y + 170 + x = 360

Now, substitute the possible values of x into the equation and solve for y.

For x = 115:
2y + 170 + 115 = 360
2y + 285 = 360
2y = 75
y = 37.5

For x = 225:
2y + 170 + 225 = 360
2y + 395 = 360
2y = -35
y = -17.5

Since angles cannot be negative, the only valid solution is y = 37.5.

Therefore, the angle measurement of Angle 2 is 37.5 degrees.