Question

In the diagram SOP ~ GNQ. find the value of x.

Answer 1

86-382+82x63

Step-by-step explanation:

Answer 2

The value of
`\(x\)` in the diagram
`\(SOP \sim GNQ\)` can be found using the property of similar triangles. Since
`\(SOP \sim GNQ\),` the corresponding angles are equal, and we can set up the proportion
`\((SO)/(GN) = (OP)/(NQ)\)` to find
`\(x\).`

Step-by-step explanation:

In similar triangles, corresponding angles are equal, and corresponding sides are in proportion. Given the similarity of triangles
`\(SOP\) and \(GNQ\)` (denoted as
`\(SOP \sim GNQ\)),` we can use the properties of similar triangles to find the value of
`\(x\)`.

The corresponding sides are
`\(SO\), \(GN\), \(OP\),`and
`\(NQ\).` According to the proportionality property, the ratio of corresponding sides is equal. Therefore, we can set up the proportion
`\((SO)/(GN) = (OP)/(NQ)\)` and solve for
`\(x\).`

Let
`\(SO = a\), \(GN = b\), \(OP = c\), and \(NQ = d\).` The proportion becomes
`\((a)/(b) = (c)/(d)\).` To find
`\(x\),` we can substitute the given values into this proportion. For example, if
`\(a = 3\), \(b = 6\), \(c = 5\), and \(d = x\), we get \((3)/(6) = (5)/(x)\).` Solving for
`\(x\),` we find
`\(x = 10\).` This process can be applied using the specific values provided in the diagram to determine the value of
`\(x\).`

In summary, the value of
`\(x\) in the diagram \(SOP \sim GNQ\)` is found using the proportionality property of similar triangles. By setting up the proportion
`\((SO)/(GN) = (OP)/(NQ)\)` and substituting the specific values, the solution for
`\(x\)` can be determined, providing insight into the relationships between corresponding sides in similar triangles.