Final answer:
To find the measures of two angles forming a linear pair where one angle is 2.6 times the other, set up an equation x + 2.6x = 180. Solving for x gives 50 degrees, so the smaller angle is 50 degrees and the larger angle is 130 degrees.
Step-by-step explanation:
This is asked to find the measure of each angle in a linear pair, where one angle is 2.6 times the measure of the other angle. In a linear pair, the angles add up to 180 degrees. Let's denote the smaller angle as 'x'. Therefore, the larger angle would be '2.6x'. The equation to find the values of 'x' and '2.6x' is: x + 2.6x = 180, 3.6x = 180, x = 180 / 3.6, x = 50. So, the smallest angle (x) is 50 degrees, and the largest angle (2.6x) is 2.6 * 50 = 130 degrees.