Question

an angle x is such that half of its complement is equals to one third of its supplement find the value of x​

Answer 1

Appropriate Question:

An angle x is such that half of its complement is equals to one fifth of its supplement. Find the value of x.

Answer:

30°

Step-by-step explanation:

As per the provided information in the given question, we have :

• An angle x is such that half of its complement is equals to one fifth of its supplement.

We are asked to calculate the value of x. Here, the half of the complement of angle x is equals to one fifth of the angle x's supplement.

If the sum of two angles is 90°, then they are called complimentary angles to each other. So, the complement of angle x will be given by the expression (90 - x)°.

If the sum of two angles is 180°, then they are called supplementary angles to each other. So, the supplement of angle x will be given by the expression (180 - x)°.

Now, according to the question the half of the complement of angle x is equals to one fifth of the angle x's supplement. Writing it in the form of an equation,

$\longmapsto \rm { \dfrac{1}{2}(90 - x)^\circ = \dfrac{1}{5}(180 - x)^\circ }$

Taking the L.C.M in both the L.H.S and R.H.S and simplifying further.

$\longmapsto \rm { \dfrac{90^\circ - x^\circ }{2} = \dfrac{180^\circ - x^\circ}{5} }$

By using the cross multiplication method, balancing the equation.

$\longmapsto \rm { 5(90^\circ - x^\circ) = 2(180^\circ - x^\circ)}$

Using the distributive property and multiplying the values.

$\longmapsto \rm { 450^\circ - 5x^\circ = 360^\circ - 2x^\circ}$

Transposing the like term from L.H.S to R.H.S and vice-versa.

$\longmapsto \rm { 450x^\circ - 360^\circ= -2x^\circ+ 5x^\circ }$

Performing addition and subtraction in L.H.S and R.H.S.

$\longmapsto \rm { 90^\circ= 3x^\circ }$

Transposing 3 from R.H.S to L.H.S.

$\longmapsto \rm { \dfrac{ 90^\circ}{3} = x^\circ }$

Dividing 90 by 3.

$\longmapsto \bf { 30^\circ = x^\circ }$

∴ The value of x is 30°.

Answer 2

Answer:

30°

Step-by-step explanation:

You are right friend.