Sum and Difference of Angles: Identifying and defining elements

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

$30+60+90=180$

The sum of the angles equals 180, therefore they can form 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.

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.

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

$90+90=180$

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 $180^\circ$.

• Step 3: Conclusion
  

  Therefore, when adjacent angles form a linear pair on a straight line, their sum is indeed $180^\circ$.

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.

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.

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.