Respuesta :
1. Angles 2, 3 and angles 1,3 are complementary angles(Given)
2. To prove : [tex] m\angle 1=m\angle 2 [/tex]
Since Angles 2, 3 and angles 1,3 are complementary.
When angles are complementary, then the sum of the measures of angles is 90 degrees.
So, [tex] m\angle 1+m\angle 3=90^{\circ} [/tex] and [tex] m\angle 2+m\angle 3=90^{\circ} [/tex] (Definition of Complementary angles)
3. [tex] m\angle 1+m\angle 3=m\angle 2+m\angle 3 [/tex] (Substitution)
4. [tex] m\angle 1=m\angle 2 [/tex] (Subtraction property of equality)
Refer the below solution for better understanding.
Step-by-step explanation:
Given :
[tex]\angle 2, \angle 3[/tex] and [tex]\angle 1, \angle 3[/tex] are complementary angles.
To Prove :
[tex]\rm m\angle 1 = m\angle2[/tex]
Given that [tex]\angle 2, \angle 3[/tex] and [tex]\angle 1, \angle 3[/tex] are complementary angles and if angles are complementary than sum of the measure of angles theire is [tex]90^\circ[/tex].
Therefore, [tex]\rm m\angle 2 +m \angle 3 = 90^\circ[/tex] and [tex]\rm m\angle 1 +m \angle 3 = 90^\circ[/tex] because they are complimentary angles.
[tex]\rm m\angle 2 +m \angle 3 = \rm m\angle 1 +m \angle 3[/tex] due to Substitution
[tex]\rm m\angle 2 =m \angle 1[/tex] due to subtraction property of equality.
For more information, refer the link given below
https://brainly.com/question/13954458?referrer=searchResults
