Question

determine whether it is possible to draw a triangle with the given angle measures.
55°, 60°, 75°
select the answer from the drop - down list to correctly complete the sentence.
show hints
it is
to draw a triangle with the given angle measures.

Explanation:

Step1: Recall triangle angle sum

The sum of angles in a triangle is \(180^\circ\).

Step2: Calculate sum of given angles

Add the angles: \(55^\circ + 60^\circ + 75^\circ = 190^\circ\)? Wait, no: \(55 + 60 = 115\), \(115 + 75 = 190\)? Wait, no, 55+60 is 115, 115+75 is 190? Wait, no, 55+60=115, 115+75=190? Wait, that can't be. Wait, no, 55 + 60 is 115, 115 + 75: 115+70=185, +5=190. Wait, but the triangle angle sum is 180. Wait, did I miscalculate? Wait, 55 + 60 is 115, 115 + 75: 55+75=130, 130+60=190. Oh, so the sum is 190, which is more than 180. Wait, but that would mean it's not possible? Wait, no, wait, maybe I made a mistake. Wait, 55 + 60 + 75: 55+60=115, 115+75=190. So the sum is 190 degrees, which is more than 180. Therefore, it's not possible? Wait, but wait, maybe the problem is different. Wait, no, the triangle angle sum theorem states that the sum of interior angles of a triangle is 180 degrees. So if the sum of the given angles is not 180, then it's not possible. Wait, but let me check again: 55 + 60 is 115, 115 + 75: 55+75=130, 130+60=190. Yes, so 190 degrees, which is more than 180. Therefore, it's not possible to draw a triangle with these angle measures. Wait, but maybe I messed up the numbers. Wait, the problem says 55, 60, 75. Let me add again: 55 + 60 = 115; 115 + 75 = 190. So sum is 190, which is greater than 180. Therefore, it's not possible. Wait, but maybe the question has a typo? Or maybe I made a mistake. Wait, no, the triangle angle sum is a fundamental theorem. So if the sum is not 180, the triangle can't exist. So the answer is it is not possible. Wait, but let me confirm: 55 + 60 + 75 = 190, which is not 180, so the sum of the interior angles of a triangle must be 180, so it's impossible.

Answer:

not possible