Question

find the value of x. b 85° c 95° a x= x°

Explanation:

Step1: Recall the formula for the measure of an angle formed by two tangents

The measure of an angle formed by two tangents outside a circle is \( \frac{1}{2}(|x - y|)\), where \(x\) and \(y\) are the measures of the intercepted arcs. Here, the angle \( \angle ABC=85^{\circ}\), and one intercepted arc is \(95^{\circ}\), and the other is \(x^{\circ}\). Also, the sum of the measures of the arcs of a circle is \(360^{\circ}\). But we can use the formula \(m\angle ABC=\frac{1}{2}(x - 95)\) (since \(x>95\) as \(x + 95<360\) and \(x>95\) for the angle formula).

Step2: Solve the equation for \(x\)

We know that \(85=\frac{1}{2}(x - 95)\).
Multiply both sides of the equation by \(2\): \(2\times85=x - 95\).
So, \(170=x - 95\).
Add \(95\) to both sides: \(x=170 + 95\).

Answer:

\(x = 265\)