Question

what is the value of x? x + 69° 5x + 99°

Explanation:

Step1: Recall cyclic - quadrilateral property

In a cyclic quadrilateral, the sum of opposite angles is 180°. Angles at \(S\) and \(U\) are opposite angles. So, \((x + 69^{\circ})+(5x+99^{\circ})=180^{\circ}\).

Step2: Combine like - terms

Combine the \(x\) terms and the constant terms: \(x+5x + 69^{\circ}+99^{\circ}=180^{\circ}\), which simplifies to \(6x+168^{\circ}=180^{\circ}\).

Step3: Isolate the variable \(x\)

Subtract \(168^{\circ}\) from both sides: \(6x=180^{\circ}- 168^{\circ}\), so \(6x = 12^{\circ}\). Then divide both sides by 6: \(x=\frac{12^{\circ}}{6}\).

Answer:

\(x = 2^{\circ}\)