Answer :
Final answer:
To find the measure of each angle, we need to understand the concepts of complementary, supplementary, vertical, and adjacent angles. Complementary angles add up to 90 degrees, supplementary angles add up to 180 degrees, vertical angles have equal measures, and adjacent angles share a common vertex and side. The measure of an angle is found by solving the equation where it is forty-nine times its supplementary angle. In this case, the angle measures 176.4 degrees.
Explanation:
Measure of Complementary Angles:
Complementary angles add up to 90 degrees. Let's assume one angle is x. So, the other angle will be 90 - x.
Measure of Supplementary Angles:
Supplementary angles add up to 180 degrees. If one angle is x degrees, then the other angle will be 180 - x degrees.
Measure of Vertical Angles:
Vertical angles are formed by two intersecting lines and have equal measures. So, if one angle is x degrees, then the other angle will also be x degrees.
Measure of Adjacent Angles:
Adjacent angles are two angles that share a common vertex and a common side. There is no specific formula to find adjacent angles as their measures can vary depending on the given information.
Given Information:
The measure of an angle is forty-nine times the measure of its supplementary angle.
Solution:
Let's assume the measure of the angle is x degrees. According to the given information, the measure of its supplementary angle will be 180 - x degrees. So, we can write the equation:
x = 49(180 - x)
Solving this equation, we get:
x = 49(180 - x)
x = 8820 - 49x
50x = 8820
x = 176.4
Therefore, the measure of the angle is 176.4 degrees.
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