7 characteristics of the obtuse angle

Once again, we bring you a new geometry lesson from a Teacher. Specifically, we are going to deal with the issue of obtuse angle characteristics. To start, we'll review what an angle is and what makes it obtuse. Next, we will see what aspects characterize it in a more concrete way. Finally, we will see some abstract examples and some more everyday ones, before proposing an exercise and its respective solutions.

Index

1. What is an obtuse angle
2. What are the characteristics of the obtuse angle
3. examples of obtuse angles
4. exercise on obtuse angles
5. Solution to exercises

An angle is the opening between two lines joined by a vertex, which can be of different sizes. The obtuse angle is the one that measures more than 90º, but less than 180º. That is, it is greater than a right angle, but less than a straight angle: it is called an obtuse angle.

To easily and graphically identify this type of angle, we can divide a circumference into four parts, as if they were the quarters of a clock. The obtuse angle is one that exceeds a quarter of that circumference, but does not reach half.

The characteristics of the most relevant obtuse angles (and that help us to identify them) are the following:

1. measure between 90º and 180º, both not included.
2. Its complementary angle will always be a acute angle.
3. An obtuse angle will never be complementary from another angle.
4. The lines that form it will never be perpendicular.
5. They have a vertex.
6. They are measured using a conveyor of angles or a bevel and a set square.
7. A triangle is considered obtuse if it has at least an obtuse angle.

Now that we know the characteristics of the obtuse angle, it is important that we see clear examples. As far as examples of obtuse angles are concerned, we can see numerical examples and more graphic examples. The first could be:

• 132º
• 112º
• 96º
• 129º
• 98º
• 169º
• 91º
• 135º

As more everyday examples:

• A beach chair.
• A very open laptop.
• On an analog clock, when the small hand is at eight and the large hand is at twelve, an obtuse angle is created.
• Very open scissors.

Let's check if you have correctly understood what an obtuse angle is and what its characteristics are through some exercises. solve these obtuse angle exercises and check the solutions below:

1. Determine if the following sentences are true or false:

• An angle of 190º is obtuse.
• Obtuse angles never have a complement.
• An obtuse angle is always more open than a right angle.
• A right angle can be considered obtuse in some cases.

2. Determine which are obtuse angles:

• 45º
• 145º
• 245º
• 345º

3. Find 3 everyday examples of obtuse angles.

Let's see if you have carried out the proposed activities correctly:

1. Determine if the following sentences are true or false:

• An angle of 190º is obtuse: false, because obtuse angles are greater than 90º, but less than 180º.
• Obtuse angles never have complementary: true, since the complementary angle is the one that helps to reach 90º, as the obtuse angles are always greater than 90º, they cannot have complementary or be.
• An obtuse angle is always more open than a right angle: true, but taking into account that it must be smaller than a straight angle.
• A right angle can be considered obtuse in some cases: false, since a right angle always measures 90º and an obtuse angle must measure more than 90º, so that one type of angle is totally incompatible with the other. other.

2. Determine which are obtuse angles:

• 45º
• 145º
• 245º
• 345º

Of the proposed angles, only the 145º angle is obtuse, since the 45º angle is less than 90º and the 245º and 345º angles are greater than 180º.

3. Find 3 everyday examples of obtuse angles.

Open response at the discretion of the student.

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