One angle of a triangle is one third of the other and the third angle is 19° more than the greater of two angles. Find the three angles of the triangle.
Answers
Answer:
Step-by-step explanation:
Cosider one angle =x
Other angle is =1/3 of x=x/3
Obviously the angle x/3 is smaller than the angle x.
Third angle is 19 degrees more than the greater angle of previous two angles.
The greater angle between the angle x and angle x/3 is x.
So third angle is 19+x.
Now the three angles are x,x/3,19+x
As we know, sum of angles of a triangle is 180.
So x+x/3+19+x=180
x+x/3+x+19=180
2x+x/3=180-19
(6x+x)/3=161
7x/3=161
x=(3*161)/7
x=3*23
x=69
One angle is 69
Other angle is 1/3 of other
So 1/3 of 69 is (1/3)*69=23
Third angle is 19 degrees more than the greater angle.
Greater angle of previous two angles is 69. So third angle is 69+19=88.
So to check the answer add all the three angle and find whether it is coming equal to 180.
69+23+88=180.
So the answe is correct.
The three angles are 69,23,88 degrees
Answer:
let's one angle be 1x
their second angle = 1/3x
third angle = x+19° (x > 1/3x
So,
3x+x/3x+180° [ angle sum property ]
3x+x+x / 3 = 180°- 19
==> 7x/3 = 161
==> 7x= 161 ×3
=> 7x = 483
=>> x = 483 / 7
==>> x = 690
second angle = 69 / 3 = 23°
Third angle = 69 + 19° = 38°