Question

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find the value of \\(x\\) in the given quadrilateral with interior angles \\(70^\circ\\), \\(45^\circ\\), \\(88^\circ\\), and \\(x\\).

Explanation:

Identify the geometric shape

The given figure has four vertices and four straight sides, which makes it a quadrilateral.

Recall the angle sum theorem

For any quadrilateral, the sum of all interior angles is always \(360^\circ\).

Set up the equation

Let the four interior angles be \(70^\circ\), \(x\), \(88^\circ\), and \(45^\circ\).

$$ 70^\circ + x + 88^\circ + 45^\circ = 360^\circ $$

Simplify and solve for x

Combine the known angle measures:

$$ 70^\circ + 88^\circ + 45^\circ = 203^\circ $$

Substitute back into the equation:

$$ 203^\circ + x = 360^\circ $$

Subtract \(203^\circ\) from both sides:

$$ x = 360^\circ - 203^\circ = 157^\circ $$

Answer:

\(x = 157^\circ\)