Question

Mya claims (m23 + m24) = m1, as shown in the triangle below. Which equations explain why Mya's claim must be true?

A) (m1 + m2) = 90° and (m23 + m24) = 90°
B) (m21 + m2) = 180° and (m23 + m24) = 180°
C) (m21 + m2) = 90° and (m23 + m24 + m2) = 90°
D) (m1 + m2) = 180° and (m23 + m24 + m2) = 180°

Answer 1

The correct equations supporting Mya's claim are B) (m21 + m2) = 180° and (m23 + m24) = 180° because these equations adhere to the Straight Angle Theorem and the Triangle Sum Theorem respectively, showing that the angles in question sum to 180 degrees due to their positions in the triangle and on a straight line.

The right answer is B) (m21 + m2) = 180° and (m23 + m24) = 180°

Step-by-step explanation:

The problem presented is a geometry question involving triangle angle relationships. Mya's claim that (m23 + m24) = m1 must be supported by the proper sets of equations that are true for the angles in a triangle. We know that the sum of the angles in a triangle is 180 degrees, so the correct equations must reflect this property.

Option B) (m21 + m2) = 180° and (m23 + m24) = 180° satisfies this requirement because m1, m21, and m23 + m24 are angles that form a straight line and therefore must add up to 180 degrees.

Similarly, m2, m21, and m23 + m24 form the internal angles of the triangle and also must sum to 180 degrees. By the Straight Angle Theorem and the Triangle Sum Theorem, these equations must hold true, supporting Mya's claim.

The right answer is B) (m21 + m2) = 180° and (m23 + m24) = 180°