Question

how to make 50° angle with campass? ​

Answer 1

Step-by-step explanation:

No, the 50 degree angle cannot be constructed with a compass and ruler. This is why:

An angle can be constructed only if its cosine is constructible.

A number can be constructed if and only if it is a root of a polynomial with integer coefficients, is irreducible (i.e. cannot be factored into polynomials with integer coefficients) and of degree less than or equal to 2. For example, 2/3,2–√ is constructible but 3–√3 is not. Since, they are the roots of 3x−2=0,x2−2=0,x3−3=0 , respectively.

Now, we will prove that cos50∘ is the root of an irreducible polynomial with integer coefficients and degree greater than 2.

Note that,

cos3θ=4cos3θ−3cosθ

so,

cos150∘=4cos350∘−3cos50∘

let cos50∘=x, then,

−3√2=4x3−3x

or,

8x3−6x=−3–√

squaring both sides, we get:

64x6−96x4+36x2−3=0(1)

putting y=2x ,

y6−6y4+9y2−3=0(2)

further, if z=y2 , then

z3−6z2+9z−3=0(3)

Now if this polynomial can be reduced (i.e. factored) into polynomials with integer coefficients, it has a factor of degree one. This is true only if any of the factors of -3 (i.e. 3, -3, 1, -1) are a root of this polynomial. Whereas, this is not the case.

Thus we have proved that cos50∘ cannot be constructed, and hence, a 50 degree angle cannot be constructed.

Answer 2

Answer:

make an acute angle

Step-by-step explanation:

because right angle is 90° and acute angle is 50° so make it