Question

12,498 Learners found this answer helpful

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

Explanation:

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<reasoning>

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:
\[
x = 360^\circ - 203^\circ = 157^\circ
\]
</reasoning>

<answer>
\(x = 157^\circ\)
</answer>

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Answer:

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</pre_analysis>

<reasoning>

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:
\[
x = 360^\circ - 203^\circ = 157^\circ
\]
</reasoning>

<answer>
\(x = 157^\circ\)
</answer>

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