Question

Points A, B, and C form a triangle. Complete the statements to prove that the sum of the interior angles of ABC is 180º.

Statement: m₁ + m₂ + m₃ = 180°
Reason:
a) Angle addition and definition of a straight line
b) Definition of parallel lines
c) Substitution
d) All of these

Answer 1

To prove that the sum of the interior angles of triangle ABC is 180°, we can use angle addition and the definition of a straight line. Thus, the statement m₁ + m₂ + m₃ = 180° is valid.

Step-by-step explanation:

To prove that the sum of the interior angles of triangle ABC is 180°, we can use the statement: m₁ + m₂ + m₃ = 180°. The reason for this is angle addition and the definition of a straight line. When two lines intersect, they form two pairs of vertical angles, which are congruent. Therefore, we can substitute the measure of one angle with its congruent angle, resulting in m₁ + m₂ + m₃ = 180°.

So, the answer is: d) All of these.