What is the measure of an angle that is equal to its complement?

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To find the measure of an angle that is equal to its complement, we need to understand what complementary angles are. Complementary angles are two angles whose measures add up to 90 degrees.

Let’s denote the angle we are trying to find as x. According to the definition of complementary angles, the complement of x can be expressed as 90 – x.

Now, since the angle is equal to its complement, we can set up the equation:

x = 90 - x

Next, we will solve for x.

  • Add x to both sides of the equation:
x + x = 90
  • This simplifies to:
2x = 90
  • Now, divide both sides by 2:
x = 45

Therefore, the measure of the angle that is equal to its complement is 45 degrees.

In conclusion, when an angle is equal to its complement, its measure is always 45 degrees.

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