Complementary Angles

Definition

Complementary angles are two angles that add up to 90 degrees. They are adjacent angles that form a right angle when combined. This concept is essential in understanding the properties of angles, triangles, and other geometric shapes.

5 Must Know Facts For Your Next Test

1. The sum of the measures of two complementary angles is always 90 degrees.
2. Complementary angles can be used to find the measure of an unknown angle in a geometric figure, such as a triangle or a rectangle.
3. When two lines intersect, the angles formed are either complementary or supplementary.
4. Complementary angles are often used in the Pythagorean Theorem to solve for the missing side of a right triangle.
5. The properties of complementary angles are essential in understanding the relationships between angles in rectangles, triangles, and trapezoids.

Review Questions

• Explain how complementary angles are used to find the measure of an unknown angle in a geometric figure.
  • If you know the measure of one angle in a geometric figure, such as a triangle or a rectangle, and you know that the two angles are complementary, you can use this information to find the measure of the unknown angle. Since complementary angles add up to 90 degrees, you can subtract the known angle's measure from 90 degrees to find the measure of the unknown angle.
• Describe how the properties of complementary angles are used in the Pythagorean Theorem to solve for the missing side of a right triangle.
  • The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. Complementary angles are used in this theorem because the two angles that form a right triangle are complementary, and their measures add up to 90 degrees. This relationship can be used to solve for the missing side of a right triangle when the other two sides are known.
• Analyze how the properties of complementary angles are essential in understanding the relationships between angles in rectangles, triangles, and trapezoids.
  • $$\begin{align*}\text{Rectangles:} &\text{ The four angles in a rectangle are all right angles, which means they are complementary.} \\ \text{Triangles:} &\text{ The three angles in a triangle add up to 180 degrees, and any two angles in a triangle are complementary.} \\ \text{Trapezoids:} &\text{ The two base angles in a trapezoid are complementary, and the two vertex angles are also complementary.}\end{align*}$$ Understanding the properties of complementary angles is crucial in analyzing the relationships between the angles in these geometric figures and solving problems involving them.

Related terms

Adjacent Angles: Adjacent angles are two angles that share a common vertex and a common side, but do not overlap.

Right Angle: A right angle is an angle that measures exactly 90 degrees, or one-quarter of a full circle.

Supplementary Angles: Supplementary angles are two angles that add up to 180 degrees, forming a straight line.