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Chapter 1: Problem 17

The sum of the angles in a triangle is ___________ degrees.

Short Answer

Expert verified
The sum of the angles in a triangle is \(180\) degrees.

Step by step solution

01

Identify the angles

In a triangle, there are three interior angles. Let's call these angles angle A, angle B, and angle C. Step 2: Recall the property of the sum of interior angles in a triangle
02

Sum of interior angles

There is a property that states the sum of all interior angles in any triangle is always equal to 180 degrees. Step 3: Add the angles together
03

Add the angles

To find the sum of the angles in a triangle, add angles A, B, and C together using the equation: Angle A + Angle B + Angle C = 180 degrees. Answer: The sum of the angles in a triangle is \(180\) degrees.

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Key Concepts

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

Geometry Basics
Geometry is a branch of mathematics that deals with shapes, sizes, and properties of space. Understanding geometry basics is crucial, as these concepts are foundational to solving more complex problems. One essential topic in geometry is the sum of angles in shapes, especially in triangles.
  • Triangles are three-sided polygons.
  • Each triangle has three angles, which are referred to as interior angles.
  • The study of geometry begins with understanding simple shapes like triangles before moving onto more complex shapes.
By grasping these basics, students build a solid foundation for further studies in geometry and other areas of mathematics.
Properties of Triangles
Triangles have several unique properties that make them an interesting subject in geometry.
  • One key property is that their interior angles always add up to 180 degrees.
  • This property applies to all types of triangles, whether they are equilateral, isosceles, or scalene.
  • Another important property is that the length of any side of a triangle is always shorter than the sum of the lengths of the other two sides.
Understanding these properties helps students solve problems involving triangles and also allows them to explore how different types of triangles behave in various situations.
Mathematical Reasoning
Mathematical reasoning involves using logical thinking to solve problems and draw conclusions from given information. In the context of triangles, mathematical reasoning is applied to understand and prove properties such as the sum of interior angles.
  • When given a triangle, start by identifying all relevant properties and relationships.
  • Use logical steps to deduce conclusions, such as how the sum of the angles is always 180 degrees.
  • Employ equations and known properties to justify your reasoning.
Applying mathematical reasoning helps in developing a systematic approach to solving not just geometry problems but mathematical problems in general. It builds critical thinking skills essential in various academic and real-world situations.

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Most popular questions from this chapter

Applications of Perimeter, Area, and Volume: Use 3.14 for \(\pi\) and include the correct units. Phil plans to put a fence around his \(9 \mathrm{ft} \times 5 \mathrm{ft}\) rectangular garden to keep out the rabbits. The fencing costs \(\$ 1.60 / \mathrm{ft}\). How much will the fence cost?

Write a mathematical expression for each and simplify. Twice the difference of \(-5\) and \(-15\)

Rewrite each expression using the distributive property. Simplify if possible. $$-(x-4 y+10 z)$$

Rewrite each expression using the distributive property. Simplify if possible. $$2(-6+5+3)$$

Use a signed number to represent the change in each situation. In Michael Jordan's last season with the Chicago Bulls \((1997-1998)\) the average attendance at the United Center was \(23,988 .\) During the \(2002-2003\) season, the average attendance fell to \(19,617 .\) This was a decrease of 4371 people per game. (Total Basketball: The Ultimate Basketball Encyclopedia, by Ken Shouler, Bob Ryan, Sam Smith, Leonard Koppett, and Bob Bellotti, \(\oplus\) 2003, SPORT Media Pub, Inc.)
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