Question

find the missing value.
x=
answer
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Explanation:

Step1: Use the property of similar triangles

Since the two triangles are similar (by SSS similarity as the sides are in proportion), the sum of angles in a triangle is \(180^{\circ}\). But we can also use the property that vertical angles are equal and the ratio of angles based on the side - angle relationship. However, a more straightforward way is to use the fact that the sum of angles in a triangle gives \(4x + x+ x= 180\) (using the angle - sum property of a triangle. Wait, no, actually, since the triangles are similar and using the property of the sum of angles in a triangle. Wait, another approach: the two triangles are similar (by SSS similarity: if the sides of two triangles are in proportion, the triangles are similar). For the lower triangle, let's assume the base - angle theorem (but no, better use the angle - sum property. The two triangles: for the upper triangle with angle \(4x\) and the lower triangle. Wait, actually, using the property that the two triangles are similar (by SSS as the sides are marked with equal segments). Then, the angles of similar triangles are equal. But also, using the angle - sum property of a triangle. Let's consider the triangle with angle \(x\). Wait, no, actually, using the property that \(4x+x + x=180\) (sum of angles in a triangle is \(180^{\circ}\)).

Step2: Solve the equation

$$
LATEXBLOCK0
$$

Answer:

\(30\)