Question

find the value of x.

Explanation:

Step1: Identify triangle type

The triangle \( \triangle HJK \) has all three sides marked as equal (indicated by the tick marks), so it is an equilateral triangle. In an equilateral triangle, all angles are equal and each angle measures \( 60^\circ \)? Wait, no, wait—wait, the angle at \( H \) is \( 12x^\circ \). Wait, no, maybe it's an isosceles? Wait, no, three tick marks, so all sides equal, so equilateral. Wait, but maybe I misread. Wait, the diagram: \( HJ \), \( HK \), \( JK \) all have one tick? Wait, no, the original diagram: \( HJ \) has one tick, \( HK \) has one tick, \( JK \) has one tick? Wait, no, the user's diagram: looking at the triangle, \( HJ \) has a tick, \( HK \) has a tick, \( JK \) has a tick? Wait, no, maybe two sides? Wait, no, the problem: maybe it's an equilateral triangle, so all angles are \( 60^\circ \)? Wait, no, maybe the angle at \( H \) is \( 12x \), and since it's equilateral, all angles are equal. Wait, no, maybe I made a mistake. Wait, no—wait, in an equilateral triangle, all angles are \( 60^\circ \). So if \( 12x = 60 \), then \( x = 5 \)? Wait, no, wait, maybe it's an isosceles? Wait, no, the tick marks: three sides, so equilateral. Wait, but let's re-express. Wait, the triangle \( HJK \): sides \( HJ \), \( HK \), \( JK \) are all equal (tick marks), so it's equilateral. Therefore, each angle is \( 60^\circ \). So \( 12x = 60 \).

Step2: Solve for \( x \)

Set up the equation \( 12x = 60 \). Divide both sides by 12: \( x = \frac{60}{12} = 5 \).

Answer:

\( x = 5 \)