To determine if it is possible to draw a triangle with angles [tex]\(150^\circ\)[/tex], [tex]\(20^\circ\)[/tex], and [tex]\(20^\circ\)[/tex], we need to check the sum of the angles in any triangle. A fundamental property of triangles is that the sum of their interior angles must be exactly [tex]\(180^\circ\)[/tex].
Let's add the given angles:
[tex]\[ 150^\circ + 20^\circ + 20^\circ = 190^\circ \][/tex]
The sum of these angles is [tex]\(190^\circ\)[/tex]. Since the sum of the angles in a triangle must be [tex]\(180^\circ\)[/tex], and in this case, it is [tex]\(190^\circ\)[/tex], it is not possible to draw a triangle with these given angles.
Therefore, a triangle with angles [tex]\(150^\circ\)[/tex], [tex]\(20^\circ\)[/tex], and [tex]\(20^\circ\)[/tex] cannot exist because the sum of the angles is not equal to [tex]\(180^\circ\)[/tex].
