Question

in the inscribed quadrilateral qrst, m∠q = 92° and m∠r = 76°. what is the measure of ∠t? 88° 92° 76° 104°

Explanation:

Step1: Recall property of inscribed quadrilateral

Opposite angles of an inscribed quadrilateral are supplementary (sum to 180°). ∠Q and ∠S are opposite, ∠R and ∠T are opposite.

Step2: Use the supplementary - angle relationship

We know that for opposite angles ∠R and ∠T, \(m\angle R+m\angle T = 180^{\circ}\). Given \(m\angle R=76^{\circ}\), we can solve for \(m\angle T\) as \(m\angle T=180 - m\angle R\).

Step3: Calculate the measure of ∠T

\(m\angle T=180 - 76=104^{\circ}\)

Answer:

104°