Final answer:
To find the measure of each angle in a linear pair where one angle is 1 and 1/2 times the other, set up an algebraic equation representing their sum as 180 degrees. Solve for the smaller angle, then calculate the larger angle.
Step-by-step explanation:
When two angles form a linear pair, they are adjacent (share a common side) and add up to 180 degrees. Given that one angle is 1 and 1/2 times the measure of the other angle, we can use algebra to find the measure of each angle.
Step-by-Step Solution:
- Let the measure of the smaller angle be x degrees.
- Since one angle is 1 and 1/2 times the other, the larger angle will be 1.5x degrees.
- The sum of the angles in a linear pair is 180 degrees, so the equation to solve is x + 1.5x = 180.
- Combining like terms gives us 2.5x = 180.
- Dividing both sides by 2.5 gives x = 72 degrees.
- Therefore, the larger angle is 1.5 × 72 = 108 degrees.
The measures of the two angles are 72 degrees and 108 degrees.