Final answer:
Two angles forming a linear pair have measurements that add up to 180 degrees. One angle is 10 degrees more than 25% of the other. Solving this, the angles measure 136 degrees and 44 degrees respectively.
Step-by-step explanation:
When two angles form a linear pair, they are adjacent and their non-common sides form a straight line. This means that their measures add up to 180 degrees. If one angle's measure is 10 degrees more than 25% of the other angle, we can set up an equation to find their measures.
Let the measure of the first angle be x degrees. Therefore, the measure of the second angle would be 0.25x + 10 degrees. Since they form a linear pair, we can write:
x + 0.25x + 10 = 180
Combining like terms, we get:
1.25x + 10 = 180
Subtracting 10 from both sides, we find:
1.25x = 170
Dividing both sides by 1.25, we get:
x = 136
Therefore, the measure of the first angle is 136 degrees, and the measure of the second angle is:
0.25(136) + 10 = 34 + 10 = 44 degrees
The two angle measurements of the linear pair are 136 degrees and 44 degrees.