Question

question 17 of 50
the value of x is:
image of a geometric figure with angles 30° and 30°, right angles, and expressions 3x + 1, 2x + 6
options: 3, 5, 2, 4, 6

Explanation:

Step1: Identify Equal Segments

The two right triangles share a common hypotenuse, and their adjacent angles to the hypotenuse are both \(30^\circ\). By the Angle - Angle - Side (AAS) congruence criterion, the two right triangles are congruent. So, the lengths of the sides opposite the \(30^\circ\) angles (i.e., \(3x + 1\) and \(2x+6\)) are equal.

Step2: Solve for \(x\)

Set the two expressions equal to each other: \(3x + 1=2x + 6\).
Subtract \(2x\) from both sides: \(3x-2x + 1=2x-2x + 6\), which simplifies to \(x + 1=6\).
Subtract 1 from both sides: \(x+1 - 1=6 - 1\), so \(x = 5\).

Answer:

5