Question

tangent lines

what is the value of (x)?

(x = \quad^{\circ})

Explanation:

Identify the geometric properties of the triangle

The diagram shows a circle with a center point connected to two points on the circle, forming two radii. A chord connects these two points on the circle.
All three sides of this triangle are marked with congruency ticks (single tick marks on the two radii and the chord).
Therefore, the triangle is equilateral:

$$ \text{All interior angles} = 60^\circ $$

Apply the tangent-radius relationship

The line containing the angle \(x^\circ\) is tangent to the circle at the vertex of the equilateral triangle.
A radius drawn to the point of tangency is perpendicular to the tangent line:

$$ \text{Angle between radius and tangent line} = 90^\circ $$

Solve for x

The angle of \(90^\circ\) is composed of the interior angle of the equilateral triangle (\(60^\circ\)) and the adjacent angle \(x^\circ\):

$$ 60 + x = 90 $$

$$ x = 30 $$

Answer:

What is the value of \(x\)?

\(x =\) <blank>30</blank>\(^\circ\)