Question

1. refer to the diagram on the right to fill in the blank. then fill in the blanks with the appropriate answer. a.) ( m angle 1 + m angle 2 = m angle ) reason: b.) if ( overrightarrow { a l } ) bisects ( angle k a t ), then ( m angle ) ( = m angle ) reason: c.) if ( angle 1 ) and form a linear pair, and are supplementary. if ( m < 1 ) and are supplementary, then ( m < 1 + m < ) ( = 180 ) reason: d.) name an angle that forms a linear pair with ( < 3 ). e.) refer to the diagram on the right. if ( p perp a ), then, ( < 1 ) and ( < 2 ) are right angles. reason:

Explanation:

Step1: Analyze part a

By the Angle - Addition Postulate, if two angles are adjacent, the measure of the larger angle formed by them is the sum of their measures. So \(m\angle1 + m\angle2=m\angle KAT\).

Step2: Analyze part b

If a ray bisects an angle, then it divides the angle into two congruent angles. Since \(\overrightarrow{AL}\) bisects \(\angle KAT\), then \(m\angle KAL=m\angle LAT\).

Step3: Analyze part c

A linear pair of angles is formed when two adjacent angles form a straight line. If \(\angle1\) and \(\angle3\) form a linear pair, then they are supplementary. Also, if two angles are supplementary, the sum of their measures is \(180^{\circ}\). So if \(m\angle1\) and \(m\angle3\) are supplementary, then \(m\angle1 + m\angle3=180\).

Step4: Analyze part d

A linear pair is a pair of adjacent angles whose non - common sides are opposite rays. An angle that forms a linear pair with \(\angle3\) is \(\angle KAT\) (because \(\angle3\) and \(\angle KAT\) are adjacent and their non - common sides form a straight line).

Step5: Analyze part e

If a line is perpendicular to another line, then the angles formed are right angles. Since \(p\perp a\), by the definition of perpendicular lines, \(\angle1\) and \(\angle2\) are right angles.

Answer:

a. \(KAT\); Angle - Addition Postulate
b. \(KAL\); \(LAT\); Definition of angle bisector
c. \(\angle3\); \(\angle3\); \(\angle3\); Definition of supplementary angles (or linear pair)
d. \(\angle KAT\)
e. Definition of perpendicular lines