Question

7.One of the enterior angles of a triangle is 80°and the interior opposite angles are in the ratio 5:3.Find the angles of the triangle.​

Answer 1

Question :-

• One of the enterior angles of a triangle is 80°and the interior opposite angles are in the ratio 5:3.Find the angles of the triangle.

Given :-

• One of the interior angle of ∆ is 80° and other interior angle are in ratio 5 : 3

Find :-

• The angles of the traingle

Solution :-

let ,

• The ratio of interior angle be in x

So,

• 5x + 3x = 80
• 8x = 80
• x = 80/8
• x = 10

★ Substituting value of x in given ratio's ★

→ 5x = 5 × 10 = 50°

→ 8x = 8 × 10 = 80°

Now :-

• Finding all the angles of triangle

By triangles property

★ Sum of the three angles of triangles is = 180°

So,

• 50 + 30 + x = 180 $\sf$
• 80x = 180
• x = 180 - 80
• x = 100°

Hence :-

• The angles are 50° , 80° , 100°

Answer 2

Answer:

ratio of interior opposite angles = 5:3

exterior angle = sum of opposite interior angles

sum of the ratios = 5+3 = 8

angle A = 5/8 (80)= 50

angle B = 3/8(80) = 30

Sum of angles of triangle = 180

Angle A + B + C = 180

let angle c = x

50 + 30 + x = 180

80+ x = 180

x = 180-80

= 100

angle A = 50

angle B = 30

angle C = 100

hope it helps............