Questions: Find the value of (x). (x=[?])

Find the value of (x). (x=[?])
Transcript text: Find the value of $x$. \[ x=[?] \]
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Solution

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Solution Steps

Step 1: Identify the given information

We are given two triangles inscribed in a circle. Both triangles share a common side of length 5. The angles between the common side and the other two sides are both 30°. One triangle has a side length of 2, and the other has a side length of x.

Step 2: Recognize triangle congruence

Since both triangles share a common side and have the same angles adjacent to that side (30°), they are congruent by the Side-Angle-Side (SAS) theorem.

Step 3: Determine the value of x

Because the triangles are congruent, their corresponding sides are equal. Therefore, x = 2.

Final Answer

2

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