Question

In a triangle xyz angle X is 20 degree more than angle Y and 25 degree more than angle Z find angle x

Answer 1

Let the angles be x, y and z

Then, According to the question,

⇒ $\angle x$ = $\angle y$ + 20°  

⇒ $\angle y$ = $\angle x$ - 20°     ......(i)

⇒ $\angle x$ = $\angle z$ + 25°    

⇒ $\angle z$ = $\angle x$ - 25° ......(ii)

According to angle sum property of a triangle, We have ;

⇒ $\angle x + \angle y + \angle z$ = 180°       ......(iii)

⇒ $\angle x + (\angle x -20^{\circ}) + (\angle x -25^{\circ})$ = 180°  

⇒ $\angle x + \angle x - 20^{\circ} + \angle x - 25^{\circ}$ = 180°

⇒ $3 \angle x - 20^{\circ}- 25^{\circ})$ = 180°

⇒ $3 \angle x - 45^{\circ})$ = 180°

⇒ $3 \angle x$ = 180°+ 45°

⇒ $3 \angle x$ = 225°

⇒ $\angle x$ = $\frac{225^{\circ}}{3}$

⇒ $\angle x$ = $\frac{\cancel{225^{\circ}}}{\cancel{3}}$

⇒ $\angle x$ = $\frac{75^{\circ}}{1}$

∴$\angle x$ = 75°

⇒$\angle y$ = $\angle x$ - 20° = 75°- 20° = 55°

⇒ $\angle z$ = $\angle x$ - 25° = 75°- 25° = 50°

∴ Angles are x = 75° , y = 55° , z = 50°