Question

Given: ATOM is the supplement of ASUE

Conclusion: MATOM + MASUE = 180°
Why:
a. True, because the sum of supplement angles is always 180°.
b. True, because ASUE and ATOM form a linear pair.
c. False, because supplement angles can be any value, not necessarily 180°.

Answer 1

The sum of supplementary angles is always 180°, thus the statement MATOM + MASUE = 180° is true. The concept is a fundamental property in Euclidean geometry which applies to the relationship between supplementary angles.

Step-by-step explanation:

The correct answer to the student's question is 'True because the sum of supplementary angles is always 180°'.

Supplementary angles are two angles whose measures add up to 180°. This is one of the fundamental properties of supplementary angles in Euclidean geometry. If the angles are denoted as MATOM and MASUE, and given that ATOM is the supplement of ASUE, by definition their sum would be 180°. Therefore, the conclusion that MATOM + MASUE = 180° holds true.

In the context of vector addition and angles, when two vectors are at right angles, you can indeed use the Pythagorean theorem to calculate the length of the resultant vector. However, if only the angles of two vectors are known, without knowing their magnitudes, you cannot find the angle of their resultant addition vector.