Angle A is equal to 30°. Angle B is equal to 60°. Angle C is equal to 90°.
Can these angles form a triangle?
Video Solution
Step-by-Step Solution
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.
Answer
Yes
Exercise #2
Angle A equals 56°. Angle B equals 89°. Angle C equals 17°.
Can these angles make a triangle?
Video Solution
Step-by-Step Solution
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.
Answer
No.
Exercise #3
a is parallel to
b
Determine which of the statements is correct.
Video Solution
Step-by-Step Solution
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.
Answer
β,γ Colateralesγ,δ Adjacent
Exercise #4
Lines a and b are parallel.
Which of the following angles are co-interior?
Video Solution
Step-by-Step Solution
Let's remember the definition of consecutive angles:
Consecutive angles are, in fact, a pair of angles that can be found on the same side of a straight line when this line crosses a pair of parallel straight lines.
These angles are on opposite levels with respect to the parallel line to which they belong.
The sum of a pair of angles on one side is one hundred eighty degrees.
Therefore, since line a is parallel to line b and according to the previous definition: the anglesβ+γ=180
are consecutive.
Answer
β,γ
Exercise #5
Which angles in the drawing are co-interior given that a is parallel to b?
Video Solution
Step-by-Step Solution
Given that line a is parallel to line b, the anglesα2,β1 are equal according to the definition of corresponding angles.
Also, the anglesα1,γ1are equal according to the definition of corresponding angles.
Now let's remember the definition of collateral angles:
Collateral angles are actually a pair of angles that can be found on the same side of a line when it crosses a pair of parallel lines.
These angles are on opposite levels with respect to the parallel line they belong to.
The sum of a pair of angles on one side is one hundred eighty degrees.
Therefore, since line a is parallel to line b and according to the previous definition: the angles
Given that according to the definition, the vertex angles are equal to each other, it can be argued that:
115=2Now we can calculate the second pair of vertex angles in the same circle:
1=3
Since the sum of a plane angle is 180 degrees, angle 1 and angle 3 are complementary to 180 degrees and equal to 65 degrees.
We now notice that between the parallel lines there are corresponding and equal angles, and they are:
115=4
Since angle 4 is opposite to angle 6, it is equal to it and also equal to 65 degrees.
Another pair of alternate angles are angle 1 and angle 5.
We have proven that:1=3=65
Therefore, angle 5 is also equal to 65 degrees.
Since angle 7 is opposite to angle 5, it is equal to it and also equal to 115 degrees.
That is:
115=2=4=6
65=1=3=5=7
Answer
1, 3 , 5, 7 = 65°; 2, 4 , 6 = 115°
Exercise #2
Angle A equals 90°. Angle B equals 115°. Angle C equals 35°.
Can these angles form a triangle?
Video Solution
Step-by-Step Solution
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.
Answer
No.
Exercise #3
Which type of angles are shown in the figure below?
Step-by-Step Solution
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.
Answer
Alternate
Exercise #4
The lines a and b are parallel.
What are the corresponding angles?
Video Solution
Step-by-Step Solution
Given that line a is parallel to line b, let's remember 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 α=βand therefore the corresponding angles
Answer
α,β
Exercise #5
Look at the parallelogram in the diagram. Calculate the angles indicated.
Video Solution
Step-by-Step Solution
ais an alternate angle to the angle that equals 30 degrees. That meansα=30Now we can calculate: β
As they are adjacent and theredore complementary angles to 180:
180−30=150
AngleγIs on one side with an angle of 20, which means:
Since the angles are not on parallel lines, none of the answers are correct.
Answer
Ninguna de las respuestas
Exercise #2
What is the value of X given that the angles are between parallel lines?
Video Solution
Step-by-Step Solution
The angle X given to us in the drawing corresponds to an angle that is adjacent to an angle equal to 154 degrees. Therefore, we will mark it with an X
Now we can calculate:
x+154=180
x=180−154=26
Answer
26°
Exercise #3
Triangle ADE is similar to isosceles triangle ABC.
Angle A is equal to 50°.
Calculate angle D.
Video Solution
Step-by-Step Solution
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
Answer
65°
Exercise #4
What kind of triangle is shown in the diagram below?
Video Solution
Step-by-Step Solution
We calculate the sum of the angles of the triangle:
117+53+21=191
It seems that the sum of the angles of the triangle is not equal to 180°,
Therefore, the figure can not be a triangle and the drawing is incorrect.
Answer
The triangle is incorrect.
Exercise #5
Given the parallelogram.
What are alternate angles?
Step-by-Step Solution
To solve the question, first we must remember that the property of a parallelogram is that it has two pairs of opposite sides that are parallel and equal.
That is, the top line is parallel to the bottom one.
From this, it is easy to identify that angle X is actually an alternate angle of angle δ, since both are on different sides of parallel straight lines.