Question

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

Explanation:

Step1: Recall triangle - angle sum property

The sum of interior angles in a right - triangle is 180°. In the large right - triangle, one angle is 90° and another is 26°.

Step2: Find the non - right angle of the large triangle

Let the non - right angle of the large triangle be \(y\). Then \(y=180^{\circ}-90^{\circ}-26^{\circ}=64^{\circ}\).

Step3: Observe the isosceles triangle

The markings on the triangle indicate that it is an isosceles triangle. In an isosceles triangle, the base angles are equal.

Step4: Calculate the value of \(x\)

The angle \(y\) can be written as \(x + x\) (because of the equal base angles of the isosceles triangle). So \(2x=64^{\circ}\), then \(x = 32^{\circ}\).

Answer:

\(x = 32\)