Angles - Examples, Exercises and Solutions

Angle A is equal to 30°.
Angle B is equal to 60°.
Angle C is equal to 90°.

Can these angles form a triangle?

We add the three angles to see if they equal 180 degrees:

$30+60+90=180$
The sum of the angles equals 180, so they can form a triangle.

Yes

Angle A equals 56°.
Angle B equals 89°.
Angle C equals 17°.

Can these angles make a triangle?

We add the three angles to see if they are equal to 180 degrees:

$56+89+17=162$

The sum of the given angles is not equal to 180, so they cannot form a triangle.

No.

$a$ is parallel to

$b$

Determine which of the statements is correct.

Let's review the definition of adjacent angles:

Adjacent angles are angles formed where there are two straight lines that intersect. These angles are formed at the point where the intersection occurs, one next to the other, and hence their name.

Now let's review the definition of collateral angles:

Two angles formed when two or more parallel lines are intersected by a third line. The collateral angles are on the same side of the intersecting line and even are at different heights in relation to the parallel line to which they are adjacent.

Therefore, answer C is correct for this definition.

$\beta,\gamma$ Colaterales$\gamma,\delta$ Adjacent

Angle A equals 90°.
Angle B equals 115°.
Angle C equals 35°.

Can these angles form a triangle?

We add the three angles to see if they are equal to 180 degrees:

$90+115+35=240$
The sum of the given angles is not equal to 180, so they cannot form a triangle.

No.

What angles are described in the drawing?

Let's remember that vertical angles are angles that are formed when two lines intersect, and they are created at the point of intersection, opposite each other.

Vertices

Which type of angles are shown in the figure below?

Alternate angles are a pair of angles that can be found on the opposite side of a line that cuts two parallel lines.

Furthermore, these angles are located on the opposite level of the corresponding line that they belong to.

Alternate

Calculate the size of angle X given that the triangle is equilateral.

Remember that the sum of angles in a triangle is equal to 180.

In an equilateral triangle, all sides and all angles are equal to each other.

Therefore, we will calculate as follows:

$x+x+x=180$

$3x=180$

We divide both sides by 3:

$x=60$

60

What is the value of the void angle?

The empty angle is an angle adjacent to 160 degrees.

Remember that the sum of adjacent angles is 180 degrees.

Therefore, the value of the empty angle will be:

$180-160=20$

20

What angles are described in the drawing?

Since the angles are not on parallel lines, none of the answers are correct.

Ninguna de las respuestas

What angles are described in the drawing?

Since we are not given any information about the lines, we cannot define the lines as parallel.

As a result, none of the options are correct.

None of the possibilities

The lines a and b are parallel.

What are the corresponding angles?

Given that line a is parallel to line b, let us remind ourselves of the definition of corresponding angles between parallel lines:

Corresponding angles are angles located on the same side of the line that intersects the two parallels and are also situated at the same level with respect to the parallel line to which they are adjacent.

Corresponding angles are equal in size.

According to this definition $\alpha=\beta$and as such they are the corresponding angles.

$\alpha,\beta$

Triangle ADE is similar to isosceles triangle ABC.

Angle A is equal to 50°.

Calculate angle D.

Triangle ABC is isosceles, therefore angle B is equal to angle C. We can calculate them since the sum of the angles of a triangle is 180:

$180-50=130$

$130:2=65$

As the triangles are similar, DE is parallel to BC

Angles B and D are corresponding and, therefore, are equal.

B=D=65

$65$°

What is the size of angle ABC?

DBC = 100°

Given that angle DBC is equal to 100 degrees. Let's look at the letters and note that angle ABC is given and equals 40 degrees

40

Can a triangle have more than one obtuse angle?

If we try to draw two obtuse angles and connect them to form a triangle (i.e., only 3 sides), we will see that it is not possible.

Therefore, the answer is no.

No

What is the size of angle ABC?

In order to calculate the value of angle ABC, we must calculate the sum of all the given angles.

That is:

$ABC=60+50$

$ABC=110$

110