Answer:
α= 22°
β= 100°
Y= 50°
Step-by-step explanation:
Given are three different triangles,
In the first triangle, two of the angles are 38° and α° and the third angle would be 120°(using vertical opposite angle equal property).
We know sum of all three angles of a triangle [tex]=180[/tex]°
Substituting,
[tex]\alpha +38+120=180\\\alpha +158=180\\\alpha =180-158\\\alpha =22[/tex]
Similarly,
In the second triangle, two of the angles are 40° and 60° and the the angle we have to find is outside(β).
We know the outside angle is equal to the sum of opposite inside angles of a triangle.
Therefore,
β[tex]=40+60\\=100[/tex]
In third triangle,'Y' is inside angle of the triangle and 70° and 160° are outside.
[tex]70[/tex]° makes linear pair,
sum of linear pair angles= [tex]180[/tex]°
Therefore the angle of triangle next to [tex]70[/tex]° would be [tex]180-70=110[/tex]°
We see 'Y' is outside and opposite to both the inside angles [tex]110 \ and \ \alpha[/tex]. thus applying the property,
[tex]Y + 110 = 160\\Y=160-110\\Y=50[/tex]°
Therefore 'Y' = [tex]50[/tex]
