Question

The two angles of a triangle are in the ratio 2:3. If the third angle is 20° less than the sum of the other two angles, find the largest angle of the triangle.

Answer 1

Answer:

the largest angle of the traingle is 80 °

Step-by-step explanation:

Let ΔABC be the traingle in which :

∠A = 2x    

∠B = 3x

∠C = ( ∠A + ∠b ) - 20

∠C =  ( 2x + 3x ) - 20

∠C =  5x - 20

∠A + ∠B + ∠C = 180°  ( angle sum property )

2x + 3x +5x - 20 = 180

10x -20 = 180

10x = 180-20

10x = 200

x=200/10

x= 20

∠A = 2x = 20*2 = 40°

∠B = 3x = 20*3 = 60°

∠C = 5x-20 = 20*5-20 = 80°

Answer 2

Answer:

80°

Step-by-step explanation:

ratio: 2:3

let the two angles be 2x and 3x

then third angle be (2x+3x)-20

SUM OF ALL ANGLES IN A TRIANGLE IS 180

2x+3x+(2x+3x)-20=180

5x+5x-20=180

10x=180+20

10x=200

x=200/10

x=20

the angles are :

• 2x=2(20)

=40°

• 3x=3(20).

=60°

• (2x+3x)-20

=(5x)-20

=5(20)-20

=100-20

=80°

Therefore the largest angle is 80°

I hope this answer is helpful!!☺️☺️