Question

what are m∠r and m∠s?

m∠r = \boxed{\circ}
m∠s = \boxed{\circ}

Explanation:

Step1: Use the property of cyclic quadrilaterals

In a cyclic quadrilateral, the sum of opposite angles is \(180^{\circ}\).
For \(\angle T\) and \(\angle R\): \(m\angle T + m\angle R=180^{\circ}\)
Given \(m\angle T = 113^{\circ}\), then \(m\angle R=180^{\circ}- 113^{\circ}\)

Step2: Calculate \(m\angle R\)

\(m\angle R = 67^{\circ}\)
For \(\angle U\) and \(\angle S\): \(m\angle U + m\angle S=180^{\circ}\)
Given \(m\angle U = 114^{\circ}\), then \(m\angle S=180^{\circ}-114^{\circ}\)

Step3: Calculate \(m\angle S\)

\(m\angle S = 66^{\circ}\)

Answer:

\(m\angle R = 67^{\circ}\), \(m\angle S = 66^{\circ}\)