Questions: Figure ABCD is a kite. Find the value of x.

Figure ABCD is a kite. Find the value of x.
Transcript text: Figure $A B C D$ is a kite. Find the value of $x$.
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Solution

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Solution Steps

Step 1: Identify the properties of a kite

A kite has two pairs of adjacent sides that are equal. In this figure, AB = AD and BC = CD.

Step 2: Use the property of diagonals in a kite

The diagonals of a kite intersect at right angles (90 degrees). The diagonal BD is perpendicular to the diagonal AC.

Step 3: Set up the equation using the given expression

Since the diagonals intersect at right angles, the given expression for one of the angles formed by the diagonals is 14x - 22. This angle must be 90 degrees.

Step 4: Solve for x

Set up the equation: \[ 14x - 22 = 90 \]

Add 22 to both sides: \[ 14x = 112 \]

Divide both sides by 14: \[ x = 8 \]

Final Answer

\[ x = 8 \]

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