Question

1. find the value of x *

your answer

Explanation:

Step1: Recognize the equilateral triangle

Since two sides are equal (marked with ticks) and one angle is \(60^{\circ}\), the lower - triangle is equilateral. So all its angles are \(60^{\circ}\), and all its sides are equal.

Step2: Use the property of isosceles triangle (upper part)

The line segment divides the larger triangle into two parts. The upper triangle has two equal sides (because of the equal - side property from the lower equilateral triangle). Let's consider the angle - side relationship. The angle adjacent to the \(60^{\circ}\) angle in the upper - triangle. Since the two sides of the upper - triangle are equal (the sides that were part of the equal sides of the larger triangle), and using the fact that the line segment creates a congruent - like situation (by SSS - Side - Side - Side if we consider the equal sides and the common side of the two sub - triangles). The angle \(x\) is equal to the angle opposite to the equal side in the upper - triangle. And because of the equilateral triangle property (\(60^{\circ}\) angle in the lower part), by the property of isosceles triangle (base angles are equal) and the fact that the two sub - triangles (upper and lower) are congruent (SSS: two sides equal as marked, and the common side). So \(x = 30^{\circ}\)

Answer:

\(30^{\circ}\)