Question

in circle c, what is the value of x?
x = 112°
x = 90°
x = 68°
x = 22°

Explanation:

Step1: Recall the property of a triangle inscribed in a circle with a diameter as one side

A triangle inscribed in a circle where one side is the diameter is a right - angled triangle. So the triangle in circle \(C\) is a right - angled triangle, and one of the angles is \(90^{\circ}\).

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let the angles of the triangle be \(x\), \(68^{\circ}\), and \(90^{\circ}\). Then \(x + 68^{\circ}+90^{\circ}=180^{\circ}\).

Step3: Solve for \(x\)

$$
LATEXBLOCK0
$$

Answer:

\(x = 22^{\circ}\)