Question

An equilateral triangle UVW is drawn inside a square STUV. What is the value of VSW?​

Answer 1

Given :  An equilateral triangle UVW is drawn inside a square STUV

To Find :  value of ∠VSW

Solution:

All Sides of Square are equal  and all angles are equal to 90°

All Sides of a equilateral triangle are equal  and all angles are equal to 60°

=> ST = TU = UV = SV = UW = VW

∠SVU = 90°

∠UVW = 60°

∠SVU  = ∠UVW + ∠SVW

=> 90° = 60° + ∠SVW

=> ∠SVW = 30°

ΔSVW is an isosceles triangle

as SV =   VW

=>∠VSW = ∠VWS   ( Angles opposites to equal sides of triangle  are equal)

Sum of Angles of a triangle is 180°

=>  ∠VSW + ∠VWS + ∠SVW = 180°

=> ∠VSW + ∠VSW + 30° = 180°

=> 2∠VSW  = 150°

=> ∠VSW  = 75°

value of angle VSW is 75°

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Answer 2

Answer:

75°

Step-by-step explanation:

side of square = 90

side of equilateral triangle = 60

therefore: 90 - 60 = 30

angle sum property says that

x + x + 30 = 180

2x + 30 = 180

2x = 180 - 30

2x = 150

x = 150÷2

x = 75°

Hope This Helps.