Final answer:
To find the measure of the smaller angle in a linear pair where one angle is 3x + 5 and the other is 2x - 10, we set up and solve the equation 5x - 5 = 180. The smaller angle is 64 degrees, corresponding to option (a) 2x - 10.
Step-by-step explanation:
To find the measure of the smaller angle formed by a linear pair, we know that the sum of the angles in a linear pair is always 180 degrees. Given one angle is 3x + 5 and the other is 2x - 10, we can set up an equation: (3x + 5) + (2x - 10) = 180.
Simplifying the equation gives us 5x - 5 = 180. Solving for x gives us x = 37. Substituting this back into the expressions for each angle, we get the first angle as 3(37) + 5 = 116 degrees and the second angle as 2(37) - 10 = 64 degrees. Therefore, the smaller angle is option (a) 2x - 10, which measures 64 degrees.