Question

incorrect 2 tries left. please try again. find the value of x. (triangle lmk with angles at l, m marked as equal, angle at k is 3x°)

Explanation:

Step1: Identify triangle type

The triangle \( \triangle LKM \) has two equal angles (at \( L \) and \( M \)), so it's isosceles? Wait, no—wait, the angle at \( K \) is \( 3x \), and angles at \( L \) and \( M \) are equal (marked with same tick). Wait, actually, if it's an isosceles triangle? Wait, no—wait, maybe it's an equilateral? Wait, no, the marks on \( L \) and \( M \) are equal, so \( \angle L = \angle M \). But also, maybe it's a triangle with \( \angle L = \angle M \), and let's check the sum of angles. Wait, maybe it's an isosceles triangle where \( \angle L = \angle M \), and \( \angle K = 3x \). Wait, but maybe the triangle is equilateral? No, the angle at \( K \) is \( 3x \), and \( \angle L = \angle M \). Wait, maybe the triangle is isosceles with \( \angle L = \angle M \), and also, maybe \( \angle L = \angle M = 3x \)? Wait, no, the marks on \( L \) and \( M \) are equal, and the mark on \( K \) is same as... Wait, no, the tick marks: \( L \) and \( M \) have one tick, \( K \) has one tick? Wait, no, looking at the diagram, \( \angle L \) and \( \angle M \) have the same tick, and \( \angle K \) has a tick? Wait, maybe all three angles are equal? Wait, if \( \angle L = \angle M = \angle K \), then it's equilateral, so all angles \( 60^\circ \). Wait, but \( \angle K = 3x \), so \( 3x = 60 \), so \( x = 20 \)? Wait, no, maybe \( \angle L = \angle M \), and \( \angle K = 3x \), and sum of angles in triangle is \( 180^\circ \). Let's assume \( \angle L = \angle M \), so let's say \( \angle L = \angle M = y \), then \( y + y + 3x = 180 \). But if the triangle is isosceles with \( \angle L = \angle M \), and also, maybe \( \angle L = \angle M = 3x \)? Wait, the tick marks: \( \angle L \) and \( \angle M \) have the same tick, \( \angle K \) has the same tick? Wait, maybe all three angles are equal (equilateral triangle), so each angle is \( 60^\circ \). So \( 3x = 60 \), so \( x = 20 \). Wait, let's check: sum of angles in triangle is \( 180 \). If \( \angle K = 3x \), and \( \angle L = \angle M = 3x \) (if all angles equal), then \( 3x + 3x + 3x = 180 \), so \( 9x = 180 \), \( x = 20 \). Yes, that makes sense. So step 1: sum of angles in triangle is \( 180^\circ \). Step 2: since all three angles are equal (equilateral triangle, as all tick marks are same), so \( 3x + 3x + 3x = 180 \) (or \( 3 \times 3x = 180 \)? Wait, no, \( \angle K = 3x \), \( \angle L = 3x \), \( \angle M = 3x \), so total \( 3x + 3x + 3x = 9x = 180 \), so \( x = 180 / 9 = 20 \). Wait, that's correct. So step 1: sum of angles in triangle is \( 180^\circ \). Step 2: set up equation \( 3x + 3x + 3x = 180 \) (or \( 3 \times 3x = 180 \)? No, \( 3x \) is one angle, and two other angles are equal to \( 3x \)? Wait, no, the tick marks: \( \angle L \) and \( \angle M \) have the same tick, \( \angle K \) has the same tick as them? So all three angles are equal. So each angle is \( 3x \), so three angles: \( 3x \), \( 3x \), \( 3x \). Sum: \( 9x = 180 \), so \( x = 20 \).

Step1: Recall triangle angle sum

The sum of interior angles in a triangle is \( 180^\circ \).

Step2: Analyze angle marks

The triangle has equal angle marks at \( L \), \( M \), and \( K \), so it's equilateral (all angles equal). Thus, each angle is \( 3x^\circ \).

Step3: Set up equation

Sum of angles: \( 3x + 3x + 3x = 180 \) (or \( 3(3x) = 180 \)? No, \( 3x \) per angle, three angles: \( 3x + 3x + 3x = 9x = 180 \)).

Step4: Solve for \( x \)

\( 9x = 180 \)
\( x = \frac{180}{9} = 20 \).

Answer:

\( \boldsymbol{20} \)