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 than ∠S.

So ∠T = ∠S – 5°

= (x + 10)° – 5°

= x + 10° – 5°

By angle sum property of triangle, sum of three angles = 180°

∠R + ∠S + ∠T = 180°

x + x + 10° + x + 5° = 180°

3x + 15° = 180°

3x = 180° – 15°

x = `(165^circ)/3` = 55°

∠R = x = 55°

∠S = x + 10° = 55° + 10° = 65°

∠T = x + 5° = 55° + 5° = 60°

∴ ∠R = 55°

∠S = 65°

∠T = 60°