Final answer:
The measures for the two angles are 5 degrees and 175 degrees. This result is found by understanding that the sum of angles in a linear pair is 180 degrees, and then applying algebra to solve for the given condition that one angle is 5 degrees less than its linear pair complement.
Step-by-step explanation:
If one angle is 4x degrees and another angle is 5 degrees less than a linear pair, we can determine the measures of these angles. The sum of the angles in a linear pair is always 180 degrees. Therefore, if we denote the first angle as 4x, then the second angle must be 180 - 4x degrees. However, we are told that the second angle is also 5 degrees less than this value. So the actual angles are as follows:
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- First angle: 4x degrees
- Second angle: (180 - 4x) - 5 degrees
Combining the expressions for both angles gives us:
4x + 180 - 4x - 5 = 180
Simplifying this we get:
180 - 5 = 175
Thus, the second angle is 175 degrees. Now, to find the first angle, we can use the expression 4x = 180 - 175, which simplifies to:
4x = 5
Dividing both sides by 4 gives us:
x = 1.25
Hence, the first angle is 4x, which is 4 * 1.25 = 5 degrees. So the angles are 5 degrees and 175 degrees, respectively