Final answer:
To find the measures of the two angles forming a linear pair, we set up the equation x + (2x + 4) = 180 and solve for x. The smaller angle measures 58.67 degrees, and the larger angle measures 121.33 degrees.
Step-by-step explanation:
The question involves finding the measure of two angles that form a linear pair, with one angle being four more than twice the measure of the other. In mathematics, angles that form a linear pair are supplementary, meaning they add up to 180 degrees. Let's denote the measure of the smaller angle as x degrees. Therefore, the measure of the larger angle would be 2x + 4 degrees, according to the given information.
Now, we can set up the equation: x + (2x + 4) = 180.
Solving this equation:
Combine like terms: 3x + 4 = 180.
Subtract 4 from both sides: 3x = 176.
Divide both sides by 3: x = 58.67, which is the measure of the smaller angle.
Now we can find the larger angle by plugging x into 2x + 4: 2(58.67) + 4 = 121.33 degrees.
Therefore, the measures of the two angles are 58.67 degrees and 121.33 degrees.