Question

find values of x and y in each figure​

Answer 1

Answer:

(a). 105°+x=180°{linear pair]

x=180°-105°

x=75°

therefore,

x+y+45°=180°{Angle sum property of a triangle}

75°+y+45°=180°

y+120°=180°

y=180°-120°

y=60°

therefore, x=75°and y=60°

(b). x=75°{Vertically opposite angles}

y+x+40°=180°{Angle sum property of a triangle}

y+75°+40°=180°

y+115°=180°

y=180°-115°

y=65°

therefore, x=75°and y=65°

(c). angle BAC=x{vertically opposite angle)

angle ABC=x(Vertically opposite angle)

angle ACB=x(Vertically opposite angle)

Now In ∆ABC,.

angle BAC+Angle ABC+Angle ACB=180°{Angle sum property of a triangle}

x+x+x=180°

3x=180°

x=180°/3

x=60°

Again,

y+x=180°{linear pair]

y+60°=180°

y=180°-60°

y=120°

therefore, x=60° and y=120°