Question

in circle t, what is the value of x?
x = 19°
x = 20°
x = 24°
x = 29°

Explanation:

Step1: Recognize the right angle

The triangle formed has a side as the diameter, so the inscribed angle subtended by the diameter is a right angle ($90^\circ$).

Step2: Sum of angles in triangle

In a triangle, the sum of angles is $180^\circ$. Let the right angle be $90^\circ$, one angle is $71^\circ$, and the unknown is $x$. So $90 + 71 + x = 180$.

Step3: Solve for x

Simplify: $161 + x = 180$. Subtract $161$: $x = 180 - 161 = 19$.

Answer:

$x = 19^\circ$ (Option: \(x = 19^\circ\))