World Problems: Angles and Consecutives

Question

The sum of the measures of the four angles of a parallelogram is 360 degrees. If the measure of one angle is 50 degrees, find the measure of each of the other angles.

Answer 1

Given that a parallelogram consists of two sets of parallel lines (across from each other), there are also two sets of equal angles (diagonal from each other). If one angle measures 50 degrees, the angle diagonal to it also measures 50 degrees.

Since the total measure of the four angles is 360 degrees, and two diagonal angles measure 50 plus 50 degrees, the total of the remaining angles is:

360 degrees - 2 * 50 degrees = 360 - 100 = 260 degrees

The remaining 260 degrees need to be divided by 2:

260 / 2 = 130 degrees each (the other diagonal angles).

Checking the totals: 50 + 50 + 130 +130 = 360 degrees.