Answer :

The value of x in the given figure is x = 7.

Given is a figure with two lines intersecting at a point and making two angle (x+16) and (4x-5).

We need to find the value of x.

To find the value of x, we can set the two angles equal to each other since they are formed by the intersecting lines and hence are vertically opposite angles.

Vertically opposite angles are always equal to each other. In other words, if you measure one of the vertically opposite angles, it will have the same measure as its opposite angle.

According to the given information, the angles are (x+16) and (4x-5). Therefore, we can set up the following equation:

x + 16 = 4x - 5

To solve for x, we'll isolate it on one side of the equation.

Let's solve the equation step by step:

x - 4x = -5 - 16 (subtract x from both sides and simplify)

-3x = -21 (combine like terms)

x = (-21) / (-3) (divide both sides by -3)

Simplifying further, we get:

x = 7

Therefore, the value of x is 7.

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X= 7

This is how-
(x+16) = (4x-5)
(-x+16) = (4x+5)
(16+5) = (4x-x)
21 = 3x
7 = x

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