Question

136 +xX + 56Name the relationship between the pair of angles and find the value of x.Vrelationship between the angles: choose your answer...Xtype your answer.choose your answer...Previoussame-side (consecutive)interior anglesalternate interior anglesvertical anglesalternate exterior anglescorresponding angles

Answer 1

From the figure given we can see that

AE= EC

Since E is the midpoint of AC

From the figure given we can see that :

AB= CB

And since EB is equal for both then we have the following criteria SSS, then we can conclude that both angles are similar

Since are similar then:

<4= <1 = 54º

From the definition of sum of angles in a triangle we have this:

54+ 54+ <1 +<2 = 180

<1+ <2 = 72º

And by similarity then <1= <2= 72/2= 36º

then we can find angle 3 on this way:

54+36+ <3 = 180

<3= 180-54-36= 90º

Angle 1 = 54º ; Angle 2= 36º; Angle 3= 90º ; Angle 4= 54º