Question

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 degrees

Answer 1

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°.

Answer 2

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°