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
Answers
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°.
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°