Question

find the value of x.
if necessary, you may learn what the markings on a figure indicate.

Explanation:

Step1: Identify congruent triangles

The two triangles are congruent (marked with equal sides). So the angle corresponding to \(29^{\circ}\) in the second triangle is also \(29^{\circ}\).

Step2: Use triangle angle - sum property

In an isosceles triangle (the second triangle with two equal sides), let the base angles be \(29^{\circ}\) each. By the triangle angle - sum property (\(a + b + c=180^{\circ}\) for a triangle with angles \(a\), \(b\), \(c\)).
Let \(x\) be the vertex angle. Then \(x + 29^{\circ}+29^{\circ}=180^{\circ}\).

$$x=180^{\circ}-(29^{\circ}+29^{\circ})$$

$$x = 180^{\circ}-58^{\circ}$$

Answer:

\(122\)