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.
Answers
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:
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!!☺️☺️