Question

what are m∠s and m∠t?

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

Explanation:

Step1: Use the property of cyclic quadrilaterals

In a cyclic quadrilateral, the sum of opposite angles is \(180^{\circ}\).

Step2: Find \(m\angle S\)

Since \(\angle R\) and \(\angle S\) are opposite angles in a cyclic quadrilateral, \(m\angle R + m\angle S=180^{\circ}\). Given \(m\angle R = 84^{\circ}\), then \(m\angle S=180^{\circ}- 84^{\circ}=96^{\circ}\).

Step3: Find \(m\angle T\)

Since \(\angle Q\) and \(\angle T\) are opposite angles in a cyclic quadrilateral, \(m\angle Q + m\angle T=180^{\circ}\). Given \(m\angle Q = 102^{\circ}\), then \(m\angle T=180^{\circ}-102^{\circ}=78^{\circ}\).

Answer:

\(m\angle S = 96^{\circ}\)
\(m\angle T = 78^{\circ}\)