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The larger of two supplementary angles exceeds the smaller by 28 degrees. Find the angles.

Last updated date: 13th Jul 2024
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Hint: Supplementary angles are those angles which add up to 180 degrees. Thus, we use this fact to solve the above given problem. We start by assuming that the smaller angle is x degrees.

Complete step-by-step answer:
Next, we try to understand the given information in the question. It is given that one of the angles is greater than the other by 28 degrees. We start by assuming that the smaller angle is x degrees. Now, from the given information in the question, since, larger angle is greater than 28 degrees, the larger angle is (x+28) degrees.
Now, we use the definition of supplementary to further evaluate the value of x. Thus, the sum of the smaller and larger angles would be 180 degrees. Thus, we have,
   x\text{ }+\text{ }\left( x+28 \right)\text{ }=\text{ }180 \\
   2x\text{ }+\text{ }28\text{ }=\text{ }180 \\
   2x\text{ }=\text{ }180\text{ }-\text{ }28 \\
   2x\text{ }=\text{ }152 \\
   x\text{ }=\text{ }76 \\
Thus, the smaller angle is 76 degrees. (since x is equal to the smaller angle)
Now, since the larger angle is (x+28), the value of the larger angle is (76+28) = 104 degrees. Thus, we get the values of supplementary angles in the question as 76 degrees (the smaller angle) and 104 degrees (the larger angle).
Note: The common mistake that can be made in this type of question is the unfamiliarity with the term supplementary angles. One can easily confuse this with complementary angles, in which case, the sum of the angles adds up to 90 degrees. Thus, one should be clear of these terms while solving these problems.