Find the angle complementary to the angle 80.
Understand the Problem
The question is asking for the complementary angle of 80 degrees. In geometry, two angles are complementary when their sum is 90 degrees. To find the complementary angle, we subtract 80 from 90.
Answer
The complementary angle of 80 degrees is $10$ degrees.
Answer for screen readers
The complementary angle of 80 degrees is $10$ degrees.
Steps to Solve
- Identify the relationship between complementary angles
Complementary angles sum up to 90 degrees. To find the complementary angle of a given angle, we can use this relationship.
- Set up the equation
We need to find the complement of 80 degrees. We can represent the complementary angle as $x$. Thus, we set up the equation: $$ x + 80 = 90 $$
- Solve for the complementary angle
Now, we will solve the equation for $x$. We do this by subtracting 80 from both sides: $$ x = 90 - 80 $$
- Calculate the value
Now we can calculate the value of $x$: $$ x = 10 $$
The complementary angle of 80 degrees is $10$ degrees.
More Information
Complementary angles are always used in right triangle trigonometry and are important in various geometric relationships.
Tips
- A common mistake is forgetting that complementary angles sum up to 90 degrees instead of 180 degrees, which is the case for supplementary angles.
- Another mistake is not subtracting the angle properly from 90 degrees.
