Question

In ∆RST, ∠S is 10° greater than ∠R and ∠T is 5° less than ∠S, find the three angles of the triangle.

Answer 1

In ∆RST. 

Let ∠R = x. 

Then given S is ∠10° greater than ∠R 

∴ ∠S = x + 10° 

Also given ∠T is 5° less then ∠S. 

So ∠T = ∠S – 5° 

= (x + 10)° – 5° 

= x + 10° – 5° 

By angle sum property of triangles, sum of three angles = 180°.

∠R + ∠S + ∠T = 180° 

x + x + 10° + x + 5° = 180° 

3x + 15° = 180° 

3x = 180° – 15°

x = \(\frac{165°}{3}\)

= 55° 

∠R = x 

= 55° 

∠S = x + 10° 

= 55° + 10° 

= 65° 

∠T = x + 5° 

= 55° + 5° 

= 60° 

∴ ∠R = 55° 

∠S = 65° 

∠T = 60°