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
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 #5
What angles are described in the drawing?
Step-by-Step Solution
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.
Answer
Vertices
Question 1
Which type of angles are shown in the figure below?
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 α=βand as such they are the corresponding angles.
Answer
α,β
Exercise #12
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 #13
What is the size of angle ABC?
DBC = 100°
Video Solution
Step-by-Step Solution
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
Answer
40
Exercise #14
Can a triangle have more than one obtuse angle?
Video Solution
Step-by-Step Solution
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.
Answer
No
Exercise #15
What is the size of angle ABC?
Video Solution
Step-by-Step Solution
In order to calculate the value of angle ABC, we must calculate the sum of all the given angles.