Question

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

Explanation:

Step1: Use the property of isosceles triangle

The triangle with the \(28^{\circ}\) angle is isosceles (marked with equal - length sides). Let the base - angles of this isosceles triangle be \(y\). Using the angle - sum property of a triangle (\(y + y+28^{\circ}=180^{\circ}\)), we can find \(y\).

$$2y=180^{\circ}- 28^{\circ}$$

$$y = 76^{\circ}$$

Step2: Use the property of adjacent angles

The angle adjacent to \(y = 76^{\circ}\) in the other isosceles triangle (marked with equal - length sides) forms a linear pair. Let the base - angles of the lower isosceles triangle be \(x\). The non - base angle of the lower isosceles triangle is \(180^{\circ}-76^{\circ}=104^{\circ}\).
Using the angle - sum property of a triangle for the lower isosceles triangle (\(x + x+104^{\circ}=180^{\circ}\)).

$$2x=180^{\circ}-104^{\circ}$$

$$2x = 76^{\circ}$$

$$x = 38^{\circ}$$

Answer:

\(x = 38\)