one angle of a triangle is two third of a right angle, the greater angle exceeds the smaller by 20 degrees. find all angles in deg

2 thoughts on “one angle of a triangle is two third of a right angle, the greater angle exceeds the smaller by 20 degrees. find all angles in deg”

1. Step-by-step explanation:

   let right angle of triangle=X

   one angle of a triangle is 2/3 of a right angle

   =2/3×x=2x/3

   greater angle exceeds the smaller by 20 degree

   =X+20

   a/q

   X+X+20+2x/3=180°

   X+X+2x/3+20=180°

   8x/3+20=180°

   8x/3=180°-20°

   8x/3=160°

   X=160×3\8

   X=20×3

   X=60°

   hence the right angle of a triangle is 60°

   smaller angle of a triangle=2X/3

   =(2×60)/3

   =120/3

   =40°

   greater angle of a triangle=X+20°

   =60+20

   =80°

   hence the right angles of a triange are

   60°,80°,40°

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2. Answer:

   60°, 50° and 70°

   Step-by-step explanation:

   Given :

   • One angle of a triangle = ⅔ of a right angle.

   • Greater angle exceeds the smaller by 20°.

   To find :

   Measure of all the angles.

   Solution :

   ⅔ of a right angle : ⅔ × 90 = 60°

   → One of the angle of triangle measures 60°.

   Now, the greater angle exceeds the smaller by 20°.

   Let, smaller angle be x° and (x+20)° be the greater one.

   Applying angle sum property of a triangle,

   x + (x+20)° + 60° = 180°

   2x + 80° = 180°

   2x = 100°

   x = 50°

   (x+20)° = 50°+20° = 70°

   Hence, the angles are 60°, 50° and 70°.

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