Which of the following could NOT be the measures of the anges of triangleA. 30,-120,-30B. 40,-40,-100C. 60,-60,-60D. 70,-50,-70
Mathematics · Middle School · Thu Feb 04 2021
Answered on
The measures of the angles of a triangle cannot include negative values because the angles in a triangle represent the amount of turn between two sides and, by definition, cannot be less than 0° or more than 180° in Euclidean geometry. Each angle in a triangle must be greater than 0° and less than 180°. The sum of all angles in a triangle must always be exactly 180°.
Looking at the provided options:
A. 30, -120, -30 - This option cannot be the measures of the angles of a triangle as it includes negative angles.
B. 40, -40, -100 - This option also includes negative angles and therefore is not possible.
C. 60, -60, -60 - Includes negative angles which is not possible.
D. 70, -50, -70 - Again, this option includes negative angles.
So, the correct answer is that options A, B, C, and D all include negative measures and therefore could NOT be the measures of the angles of a triangle