Question

In triangle abc,the measure of angle a is greater than the measure of angle b by 20 degree .if the exterior angle c is 140 degree,find the angle of triangle abc

Answer 1

20x+x=180
21x=180
x=180_21
x=159
159_140=114
114+20+1=135

Answer 2

Answer:

∠a = 80° ,∠b = 60° and ∠c = 40°

Step-by-step explanation:

Refer the attached figure

We are given that the measure of angle a is greater than the measure of angle b by 20 degree .

So, ∠a =∠b+20

Now we are given that the exterior angle c is 140°.

So, using exterior angle theorem of triangle

Exterior angle theorem : An exterior angle of a triangle is equal to the sum of the opposite interior angles.

So, ∠a+∠b=exterior ∠c

∠b+20+∠b=140°.

2∠b+20=140°

2∠b=120°.

∠b=60°

So, ∠a =∠b+20 = 60°+20°=80°

Now to find ∠c we will use angle sum property of triangle .

Angle sum property of triangle : The sum of all angles of triangle is 180°

∠a+∠b+∠c=180°

80°+60°+∠c=180°

140°+∠c=180°

∠c=180°-140°

∠c=40°

Hence ∠a = 80° ,∠b = 60° and ∠c = 40°