Question

In a triangle the second angle is one-third of the third angle and the third angle is one and a half times the first angle . what is the value of second angle​

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Answer 1

Answer:

Let angles of triangle are x, y and z deg. respectively.

Y=1/3z =1/3*1.5x

and z=1.5x.

Sum of all three angles x+y+z =180°

x+1/3*3/2x+1.5x=180°

x+1/2x+3/2x=180°

3*x=180°

x=60°, y=30° , z=90°

Step-by-step explanation:

Answer 2

Let the first, second, third angles of the triangle be A, B, C respectively.

Given that second angle is one third of the third angle,

i.e B = C/3 ⇒C=3B......(1)

Also third angle is one and half times (1+1/2 = 3/2) the first angle,

Therefore C=3A/2

From(1),

3B = 3A/2,

A=2B........(2).

SInce A, B, C are the angles of a triangle, sum of them is 180°.

A + B + C = 180

From (1) and (2)

2B + B + 3B = 180

⇒6B = 180

⇒B=30°.

Hence the second angle is 30°.