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Chapter 1: Problem 12

Find the supplement of each angle. $$59^{\circ}$$

Short Answer

Expert verified
The supplement of \(59^{\circ}\) is \(121^{\circ}\).

Step by step solution

01

Identify the given angle

The given angle is \(59^{\circ}\).
02

Subtract the given angle from \(180^{\circ}\)

To find the supplement of the given angle, subtract the given angle from \(180^{\circ}\): \[180^{\circ} - 59^{\circ}\]
03

Calculate the result

Subtract the angles: \[180^{\circ} - 59^{\circ} = 121^{\circ}\]
04

Write down the solution

The supplement of the given angle \(59^{\circ}\) is \(121^{\circ}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Angle Subtraction
Finding the supplemental angle involves using a straightforward process called angle subtraction. This concept comes into play when you need to determine the amount you must add to a given angle to make a straight angle, which measures exactly \(180^\circ\).
When you are given an angle and asked to find its supplement, you use the formula:
  • Supplementary angle = \(180^\circ - \text{given angle}\)
So, in our example, we start with \(59^\circ\).
We subtract it from \(180^\circ\):
  • \(180^\circ - 59^\circ = 121^\circ\)
This tells us that \(121^\circ\) is what's needed to create a straight line with the angle \(59^\circ\).
It's as simple as that! Just remember to always subtract from \(180^\circ\) when finding a supplementary angle.
Geometry Basics
Understanding geometry is crucial for making sense of angles and shapes. In geometry basics, we learn how different geometric figures interact; angles being one of the fundamental components.
Angles are formed where two lines meet or intersect, measured in degrees.
Some important points to remember about angles include:
  • Measured in degrees (\(^\circ\))
  • A full circle is \(360^\circ\)
  • A straight line is \(180^\circ\), giving rise to the concept of supplementary angles
  • Perpendicular lines form right angles, each being \(90^\circ\)
Using these fundamental properties, you can explore more complex geometric figures and understand phenomena such as supplementary and complementary angles.
Geometry basics pave the way for understanding broader concepts like congruency, symmetry, and angle relationships.
Degrees in a Triangle
Triangles are one of the simplest yet most versatile shapes in geometry.
It's essential to know that the sum of all angles in any triangle is always \(180^\circ\).
This rule applies no matter the type of triangle, whether it's acute, obtuse, or right-angle.
Understanding the degrees in a triangle helps you solve various geometric problems related to angles:
  • An equilateral triangle has three equal angles, each measuring \(60^\circ\).
  • A right triangle has one angle precisely \(90^\circ\), with the other two summing to \(90^\circ\).
  • The supplementary angles concept is also handy in triangles, especially when calculating angles within or outside the triangle.
Knowing that triangles' angles always sum to \(180^\circ\) provides a solid foundation for solving more elaborate problems in geometry.

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Most popular questions from this chapter

Objectives 3 and 4 A study conducted in 2000 indicated that about \(\frac{3}{5}\) of the full-time college students surveyed had consumed alcohol sometime during the 30 days preceding the survey. If 400 students were surveyed, how many of them drank alcohol within the 30 days before the survey? (Alcohol Research \& Health, The Journal of the Nat 1 Institute on Alcohol Abuse \& Alcoholism, Vol. 27, No. \(1,2003\) )

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