Geometry

Question Analysis

This question involves finding the missing angle. The main focus is on understanding the properties of parallel lines cut by a transversal and the property of angle bisector.

 

Key Concept Explanation:

When two parallel lines are cut by a transversal, alternate interior angles are on opposite sides of the transversal and inside the two lines. The key property is that alternate interior angles are congruent.

 

A straight angle is formed when two rays point in exactly opposite directions, making a straight line. It measures exactly 180 degrees.

 

An angle bisector is a ray, line, or segment that divides an angle into two congruent (equal) parts.

 

Step-by-Step Solution:

∵ ∠1, ∠2, and ∠3 are adjacent and together form a straight line. (Given)

∴ m∠1 + m∠2 + m∠3 = 180° (Angle Addition Postulate and Definition of Straight Angle)

∵ m∠1 = 40° (Given)

∴ 40° + m∠2 + m∠3 = 180° (Substitution)

∴ m∠2 + m∠3 = 140° (Substitution)

∵ Line m bisec...