Question

find the value of x.

x =

Explanation:

Step1: Apply the formula for the measure of an angle formed by two secants

The formula for the measure of an angle formed by two secants outside a circle is \(\theta=\frac{1}{2}(\text{larger arc}-\text{smaller arc})\). Here, \(74^{\circ}=\frac{1}{2}[(2x - 5)^{\circ}-31^{\circ}]\).

Step2: Multiply both sides by 2

Multiply both sides of the equation \(74=\frac{1}{2}[(2x - 5)-31]\) by 2. We get \(74\times2=(2x - 5)-31\), which simplifies to \(148 = 2x-5 - 31\).

Step3: Simplify the right - hand side

Simplify the right - hand side: \(148=2x-(5 + 31)\), so \(148=2x - 36\).

Step4: Add 36 to both sides

Add 36 to both sides of the equation: \(148+36=2x\), which gives \(184 = 2x\).

Step5: Divide both sides by 2

Divide both sides by 2: \(x=\frac{184}{2}\).

Answer:

\(x = 92\)