Question

24) Refer to the figure Find the value of X and Y.

Answer 1

`\sf x = 20 ^\circ`

`\sf y = 40 ^\circ`

Explanation:

From the given picture, we have

`\sf 2x + 3y + x = 180^\circ ...... \textsf{ Equation [1] }`

(Linear pair or straight line angles sum to 180°)

`\sf y = 2x ........ \textsf{ Equation [2]}`

(Vertically opposite angles are equal)

Let's solve for x and y using these equations:

Equation 1:

`\sf 2x + 3y + x = 180^\circ`

Combine the x terms:

`\sf 3x + 3y = 180^\circ`

Divide by 3:

`\sf x + y = (180^\circ )/(3)`

`\sf x + y = 60^\circ`

Equation 2:

y = 2x

Now we have a system of equations:

`\sf x + y = 60^\circ`

`\sf y = 2x`

Substitute the value of y from Equation 2 into Equation 1:

`\begin{aligned} &\sf x + 2x = 60^\circ \\& \sf 3x = 60^\circ \\& \sf x = (70^\circ)/(3)\\& \sf x = 20^\circ \end{aligned}`

Now substitute the value of x into Equation 2 to find y:

`\sf y = 2 * 20^\circ`

`\sf y = 40 ^\circ`

So, the solution is:

`\sf x = 20 ^\circ`

`\sf y = 40 ^\circ`

Answer 2

x = 20°

y = 40°

Explanation:

Angles on the same line add up to 180 degrees. We can see angles 2x, 3y, and x are on the same line. This means:

2x + 3y + x = 180 ⇒ 3x + 3y = 180 divide by 3 ⇒ x + y = 60

There is another line that contains the angles 3y, x, and y. This gives us our second equation:

3y + x + y = 180 ⇒ x + 4y = 180

We have two equations, or a system of linear equations. We can solve this using multiple different methods. However, let's use elimination. We need to "eliminate" the x variable. To do this, let's subtract the first equation from the second equation:

x + 4y - (x + y) = 180 - 60 ⇒ x + 4y - x- y = 120 ⇒ 3y = 120

Dividing both sides by 3, we get:

y = 40

Substituting this value back into the first equation, we get:

x + y = 60 ⇒ x + 40 = 60 ⇒ x = 20