Question

use the image to answer the question
prove that the sum of the measures of the exterior angles of the triangle is ( 360 ^ { circ } ). fill in the blanks in step 2 to complete the proof
1 point
statement
1 consider a triangle with interior angles ( angle 2 , angle 3 ), and ( angle 5 ) and corresponding exterior angles ( angle 1 , angle 4 ), and ( angle 6 )
2 ( m angle 1 + m angle 2 = 180 ^ { circ } )
( m angle 5 + m angle 6 = 180 ^ { circ } )
( m angle square + m angle square = square ^ { circ } )
3 ( ( m angle 1 + m angle 2 ) + ( m angle 5 + m angle 6 ) + ( m angle 3 + m angle 4 ) = 180 ^ { circ } + 180 ^ { circ } + 180 ^ { circ } )
4 ( ( m angle 2 + m angle 3 + m angle 5 ) + ( m angle 1 + m angle 4 + m angle 6 ) = 540 ^ { circ } )
5 ( m angle 2 + m angle 3 + m angle 5 = 180 ^ { circ } )
6 ( 180 ^ { circ } + ( m angle 1 + m angle 4 + m angle 6 ) = 540 ^ { circ } )
7 ( ( m angle 1 + m angle 4 + m angle 6 ) = 360 ^ { circ } )
reason
1 given
2 definition of linear pairs
3 addition
4 rearrange and simplify
5 triangle angle sum theorem
6 substitution
7 subtraction property of equality

Explanation:

Step1: Recall the definition of linear pairs

Linear pairs of angles are adjacent angles that form a straight line. Their measures add up to \(180^{\circ}\).

Step2: Identify the linear pair for \(\angle3\)

Looking at the image, \(\angle3\) and \(\angle4\) form a linear pair.
So, by the definition of linear pairs, \(m\angle3 + m\angle4 = 180^{\circ}\)

Answer:

\(m\angle3 + m\angle4=180^{\circ}\)