Question

Sum of three angles of a triangle ABC is 180 degree. The ratio of angle BAC, angle ABC and angleACB is 3:5:10 . If the value of angle BAC is decreased by 10 degree and the value of angle ABC is increased by 10 degree . Let’s calculate the new ratio of the three angles .

Answer 1

Answer:

the new ratio of the three angles (i.e. angle BAC, angle ABC and angle ACB ) = 1:3:5.

Step-by-step explanation:

ratio of the three angles = 3:5:10.

let, angle BAC = 3x

angle ABC = 5x

angle ACB = 10x.

so, 3x +5x+10x=180.

18x =180.

x = 10.

therefore, angle BAC=30°

Angle ABC= 50°

Angle ACB = 100°

value of angle BAC is decreased by 10°, so, angle BAC = 20°

value of angle ABC is increased by 10°,. so, angle ABC= 60°

So, ratio of angle BAC, angle ABC and angle ACB = 20:60:100

= 1:3:5.

Answer 2

Let each ratio be multiplied by x.

angle BAC=3, angle ABC=5,angle ACB=10

SO, angle BAC=3*X=3X

angle ABC=5*X=5X

angle ACB=10*X=10X

SUM OF THE ANGLES IN A TRIANGLE IS EQUAL TO 180 DEGREES

3X+5X+10X=180 DEGREES

18X =180

X=180/18

=10

THEREFORE, ANGLE BAC =3*X=3*10

=30 DEGREES

ANGLE ABC=5*10

= =50 DEGREES

ANGLE ACB=10*10 =100 degrees

condition: the value of angle BAC is decreased by 10 degrees and the value of angle ABC IS increased by 10 degrees, we get

THEREFORE, angle BAC=3O DEGREES -10

=20 DEGREES

angle ABC becomes 50+10 =60 degrees

therefore the ratio becomes

20:60:100

2:6:10