Question

Rozwiąż podane przykłady. Oblicz miary kątów ..Daje naj

Answer 1

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 $=180$°

Substituting,

$\alpha +38+120=180\\\alpha +158=180\\\alpha =180-158\\\alpha =22$

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$=40+60\\=100$

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

$70$° makes linear pair,

sum of linear pair angles= $180$°

Therefore the angle of triangle next to $70$° would be $180-70=110$°

We see 'Y' is outside and opposite to both the inside angles $110 \ and \ \alpha$. thus applying the property,

$Y + 110 = 160\\Y=160-110\\Y=50$°

Therefore 'Y' = $50$