An angle is greater than its complementary angle by 20°. What is the measure of this angle in degrees?

Introduction / Context:
This problem checks understanding of complementary angles and how to form simple linear equations from a verbal description. Complementary angles are a very common topic in basic geometry and appear frequently in aptitude tests and reasoning questions.

Given Data / Assumptions:
- Two angles are complementary if their sum is 90°.
- One angle is described as being greater than its complementary angle by 20°.
- We need to find the measure of the larger angle.

Concept / Approach:
Let the required angle be x degrees. Its complementary angle is then 90° − x degrees. The statement says that the angle x is greater than its complementary angle by 20°, so x is 20° more than 90° − x. This description translates directly into a simple linear equation that can be solved for x.

Step-by-Step Solution:
Step 1: Let the required angle be x degrees. Step 2: Its complementary angle is 90° − x degrees. Step 3: Given that x is greater than its complement by 20°, write the equation x = (90° − x) + 20°. Step 4: Simplify the right side: (90° − x) + 20° = 110° − x. Step 5: So the equation is x = 110° − x. Step 6: Add x to both sides: x + x = 110°, which gives 2x = 110°. Step 7: Divide both sides by 2 to obtain x = 55°.

Verification / Alternative Check:
If the angle is 55°, then its complement is 90° − 55° = 35°. The difference between the angle and its complement is 55° − 35° = 20°, which matches the condition in the question. Therefore 55° is verified as correct.

Why Other Options Are Wrong:
Option b, 35°, is actually the complementary angle, not the angle that is greater by 20°.
Option c, 100°, is greater than 90° and therefore cannot be complementary to any positive real angle in the sense of complementary pairs summing to 90°.
Option d, 80°, would have a complement of only 10°, giving a difference of 70°, not 20°.

Common Pitfalls:
A common mistake is to set up the equation with the roles reversed or to assume that the angles differ by 20° without checking which one is larger. Another error is confusing complementary angles (sum 90°) with supplementary angles (sum 180°). Carefully translating the verbal statement into an algebraic equation is the key skill in this type of question.

Final Answer:
The measure of the angle is 55°.