Question

1. fill in the \???\ section in the proof below. given: line ab is perpendicular to bc. proof: ∠1 is complementary to ∠2. proof: statements line ab is perpendicular to bc. angle b is a right angle. m∠b = 90 ∠1 and ∠2 are adjacent m∠1 < 90 and m∠2 < 90 ∠1 and ∠2 are complementary. reason??? definition of a perpendicular line. angle b is a right angle. definition of adjacent angles definition of acute angles definition of complementary angles. o definition of supplementary angles. o definition of interior angles. o definition of a right angle. o definition of angles formed by intersecting lines.

Explanation:

Step1: Analyze the Statement

The statement is \( m\angle B = 90 \). We need to find the reason for this.

Step2: Recall Definitions

Since \( AB \perp BC \), by the definition of perpendicular lines, the angle between them (angle \( B \)) is a right angle, and a right angle measures \( 90^\circ \). So the reason for \( m\angle B = 90 \) is the definition of a perpendicular line (which implies the angle between them is \( 90^\circ \)). Wait, no, the statement before that is "Angle B is a right angle" with reason "Definition of a perpendicular line". Then \( m\angle B = 90 \) should be from the definition of a right angle (since a right angle is defined as \( 90^\circ \)). Wait, looking at the options: the reason for \( m\angle B = 90 \) – the "Reason" column for that row. Wait, the "Statements" row is \( m\angle B = 90 \), and the "Reason" is "???". The previous statement is "Angle B is a right angle" with reason "Definition of a perpendicular line". Then \( m\angle B = 90 \) follows from the definition of a right angle (since a right angle is an angle with measure \( 90^\circ \)). Wait, the options on the left: one of them is "Definition of a right angle". Let's check the left options: the second one is "Definition of a right angle." So the reason for \( m\angle B = 90 \) is the definition of a right angle, because a right angle is defined to have a measure of \( 90^\circ \).

Answer:

Definition of a right angle.