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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 °

Substituting,

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

In third triangle,'Y' is inside angle of the triangle and 70° and 160° are outside.

° makes linear pair,

sum of linear pair angles= °

Therefore the angle of triangle next to ° would be °

We see 'Y' is outside and opposite to both the inside angles . thus applying the property,

°

Therefore 'Y' =

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step-by-step explanation: