Examples with solutions for Sum and Difference of Angles: Identifying and defining elements

Exercise #1

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

30+60+90=180 30+60+90=180

The sum of the angles equals 180, therefore 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 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

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

Answer

No.

Exercise #4

In a right triangle, the sum of the two non-right angles is...?

Video Solution

Step-by-Step Solution

In a right-angled triangle, there is one angle that equals 90 degrees, and the other two angles sum up to 180 degrees (sum of angles in a triangle)

Therefore, the sum of the two non-right angles is 90 degrees

90+90=180 90+90=180

Answer

90 degrees

Exercise #5

The sum of the adjacent angles is 180

Step-by-Step Solution

To determine if the statement that "the sum of the adjacent angles is 180" is true, follow these steps:

  • Step 1: Define Adjacent Angles

    Adjacent angles are two angles that have a common vertex and a common side but do not overlap. In geometry, when these angles form a straight line, they are known as a linear pair.

  • Step 2: Apply the Linear Pair Theorem

    The Linear Pair Theorem states that if two angles are adjacent and form a linear pair (i.e., the non-common sides form a straight line), then these angles are supplementary. This means that their sum is 180180^\circ.

  • Step 3: Conclusion

    Therefore, when adjacent angles form a linear pair on a straight line, their sum is indeed 180180^\circ.

This validates the statement that "the sum of the adjacent angles is 180" for linear pairs, making the statement True.

This corresponds to the answer choice stating: True.

Answer

True

Exercise #6

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 #7

What kind of triangle is shown in the diagram below?

535353117117117212121AAABBBCCC

Video Solution

Step-by-Step Solution

We calculate the sum of the angles of the triangle:

117+53+21=191 117+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 #8

What is the size of each angle in an equilateral triangle?

AAACCCBBB

Video Solution

Answer

60