Question

The angles of a triangle are (x-40)°,(x-20)°and[1/2x-10]°.find the value of x​

Answer 1

Answer:

100 deg. is the answer

Answer 2

⇒ Given:

The angles of a triangle are (x-40)°,(x-20)°and (1/2x-10)°.

⇒ To Find:

The value of the variable x.

⇒ Solution:

The basic concept to be used in the is question is the concept of the angle sum property of a triangle.

According to the angle sum property of a triangle, the sum of all the angles of a triangle is 180°.

This means that:

(x-40)° + (x-20)° + (1/2x-10)° = 180°

Now we can find the value of x.

$\sf{=(x-40)^o+(x-20)^o+(\dfrac{1}{2}-10)^o=180^o}$

$\sf{=x-40+x-20+\dfrac{x}{2}-10=180}$

Moving the constants to the RHS:

$\sf{=x+x+\dfrac{x}{2}=180+40+20+10}$

$\sf{=\dfrac{2x+2x+x}{2}=250}$

$\sf{=5x=500}$

$\sf{x=\dfrac{500}{5}}$

$\sf{x=100}$

∴ The value of x is 100.

⇒ Verification:

If the sum of all the angles become 180°, then our answer is correct.

x - 40 = 100 - 40 = 60°

x - 20 = 100 - 20 = 80°

1/2x - 10 = 50 - 10 = 40°

Sum:

= 60 + 80 + 40

= 140 + 40

= 180°

LHS + RHS

Hence verified!