contestada

Let ∠1, ∠2, and ∠3 have the following relationships.
∠1 and ∠2 are acute vertical angles.
∠3 is an obtuse angle adjacent to both ∠1 and ∠2.
What is the sum of the measure of ∠1 and the measure of ∠3?

Respuesta :

3 can be anything greater than (but not equal to) 90 and 1 can be anything less than (but not equal to) 90 as long as angle 3 + angle 1 = 180 degrees.
aksnkj

"The value of [tex]\angle1 +\angle3[/tex] lies between [tex]90^{\circ} < \angle1+\angle3< 180^{\circ}[/tex].

Given,  

[tex]\angle 1,\angle2, \angle3[/tex] have the following relationships.

  1. [tex]\angle 1[/tex]  and[tex]\angle2[/tex] are acute vertical angles.
  2. [tex]\angle 3[/tex] is an obtuse angle adjacent to both [tex]\angle 1[/tex] and [tex]\angle 2[/tex].

We have to find the sum of measure of [tex]\angle1[/tex] and the measure of [tex]\angle3[/tex].

Angle sum property:

We know that the angle sum property of triangle states that the sum of all angles of a triangle is equal to [tex]180 ^{\circ}[/tex].

[tex]\angle 1+\angle 2+\angle3= 180^ {\circ}[/tex]

[tex]\angle1+\angle3= 180-\angle2[/tex]

So, the value [tex]\angle1 and \angle3[/tex] is always greater than [tex]90{^\circ}[/tex] because [tex]\angle 3[/tex] is the obtuse angle and it is being added to [tex]\angle1[/tex],

so it is always greater than right angle and less than [tex]180^{\circ}[/tex].

Hence the value of [tex]\angle1 +\angle3[/tex] lies between [tex]90^{\circ} < \angle1+\angle3< 180^{\circ}[/tex].

For more details on angle sum property follow the link:

https://brainly.com/question/4316040

Otras preguntas