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Chapter 1: Problem 45

State whether each angle given in Exercises \(43-51\) is straight, right, acute, or obtuse. $$180^{\circ}$$

Short Answer

Expert verified
Straight angle.

Step by step solution

01

Identify the Type of Angle

Different types of angles are classified based on their measurements: - Right Angle: Exactly \, \(90^{\text{\circ}}\)- Acute Angle: Less than \,\(90^{\text{\circ}}\)- Obtuse Angle: Greater than \,\(90^{\text{\circ}}\) \ and \ less than \,\(180^{\text{\text{\circ}}}\)- Straight Angle: Exactly \,\(180^{\text{\circ}}\)
02

Compare Given Angle

The given angle measurement is \, \(180^{\text{\circ}}\).
03

Determine the Angle Type

Since the angle measurement is \, \(180^{\text{\circ}}\), it falls under the category of a straight angle.

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Key Concepts

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

straight angle
A straight angle is an angle with a measurement of exactly \(180^{\text{\text{掳}}}\). It is called a 'straight' angle because it forms a straight line.
Imagine you have a piece of paper and you fold it completely flat so that both ends touch each other. This is a great visual representation of a straight angle.
In mathematical terms, if we take a full circle, which is \(360^{\text{\text{掳}}}\), and split it in half, each half is \(180^{\text{\text{掳}}}\). These halves are the straight angles.
  • A straight angle does not bend.
  • It is always found in the middle of two rays that point in opposite directions.
Understanding what a straight angle is helps you identify other types of angles more easily.
angle classification
Before diving into specific types of angles, it's essential to understand how angles are classified. Angles are generally divided into four main categories:
  • Right Angle: Exactly \(90^{\text{\text{掳}}}\). It looks like the corner of a square.
  • Acute Angle: Less than \(90^{\text{\text{掳}}}\). These are 'sharp' or 'narrow' angles.
  • Obtuse Angle: More than \(90^{\text{\text{掳}}}\) but less than \(180^{\text{\text{掳}}}\). These angles look 'wide'.
  • Straight Angle: Exactly \(180^{\text{\text{掳}}}\). It forms a straight line.
Knowing these classifications helps in identifying and categorizing any angle you come across quickly. For example, from the exercise above, if you see an angle measurement of \(180^{\text{\text{掳}}}\), you will instantly know it is a straight angle.
geometry basics
Understanding basic geometry concepts like angles is crucial for progressing in mathematics. Angles are formed when two lines meet at a common point called a vertex.
Here are some terms and ideas that are important:
  • Vertex: The point where two lines or rays meet to form an angle.
  • Ray: A line with a starting point that extends infinitely in one direction.
Using these basic terms correctly helps you understand more complex geometry topics later on. For instance, considering the step-by-step solution provided, knowing that a straight angle is formed by two rays pointing directly opposite to each other at the vertex could make things clearer.
The key is to always start with these fundamental concepts and build upon them as you learn more intricate aspects of geometry.

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Most popular questions from this chapter

If \(m \angle A=(5 y)^{\circ}, m \angle B=(y+6)^{\circ},\) and \(\angle A\) and \(\angle B\) are complementary, find \(y\)

Complete each proof in Exercises \(25-28\). Given: \(B\) is the midpoint of \(\overline{A C}\) Prove: \(A B=\frac{A C}{2}\) Statements 1 __________ 2 \(\overline{A B}=B C\) 3 \(, A B+B C=A C\) 4 \(, A B+A B=A C\) 5 __________ 6 \( . A B=\frac{A C}{2}\) Reasons 1 Given 2 _________ 3 ___________ 4 _______ 5 Distributive law 6 _________

State whether each angle given in Exercises \(43-51\) is straight, right, acute, or obtuse. $$90^{\circ}$$

The puzzles are classic examples and a certain amount of deductive reasoning is required to solve them. Some of these puzzles are quite challenging, so don't be discouraged if you have trouble finding the solution immediately. Ideally they will make you think a bit and, along the way, provide a bit of entertainment. You have 3 sacks, each containing 3 coins. Two of the sacks contain real coins and each coin weighs 1 lb. The third contains counterfeit coins, and each weighs 1 lb 1 oz. A scale is available, but it can be used one time and one time only to obtain a particular measure of weight. How might you use the scale to determine which sack contains the counterfeit coins? [Note: You cannot add or subtract coins to a total because any change of reading up or down on the scale will cause it to zero out. \(]\)

The puzzles are classic examples and a certain amount of deductive reasoning is required to solve them. Some of these puzzles are quite challenging, so don't be discouraged if you have trouble finding the solution immediately. Ideally they will make you think a bit and, along the way, provide a bit of entertainment. The number of marbles in a jar doubles every minute and is full in 10 minutes. When was the jar half full?
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