This is a word problem involving supplementary angles. To solve it, we need to follow these steps:
Identify the given information and the unknown quantity. In this problem, we are given that an angle is 590 less than six times its own supplement. The unknown quantity is the measure of the angle.
Write an equation that relates the given information and the unknown quantity. We can use the fact that supplementary angles are two angles with a sum of 180°1. Let x be the measure of the angle. Then its supplement is 180 - x. The equation is:
x=6(180−x)−590
Solve the equation for the unknown quantity. We can simplify and rearrange the equation to get:
xx7xxx=6(180−x)−590=1080−6x−590=490=7490=70
Therefore, the measure of the angle is 70°.