Question

select the correct answer from each drop - down menu.
trapezoid pqrs
be inscribed in a circle because the
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(the trapezoid figure with angles: at s 65°, at p 115°, at q 115°, at r 65°)

Explanation:

Step1: Recall cyclic trapezoid property

A trapezoid can be inscribed in a circle (is cyclic) if and only if it is isosceles, and for a quadrilateral to be cyclic, the sum of each pair of opposite angles must be \(180^\circ\).

Step2: Check angle sums

• Angle at \(P = 115^\circ\), angle at \(R = 65^\circ\): \(115^\circ+ 65^\circ=180^\circ\)
• Angle at \(Q = 115^\circ\), angle at \(S = 65^\circ\): \(115^\circ + 65^\circ=180^\circ\)
• Also, in a trapezoid, if it's cyclic, base angles are supplementary and it's isosceles. Here, adjacent angles between the bases: \(115^\circ\) and \(65^\circ\) are supplementary (\(115 + 65=180\)), so the trapezoid is isosceles and can be inscribed in a circle.

Answer:

Trapezoid PQRS \(\boldsymbol{\text{can}}\) be inscribed in a circle because the \(\boldsymbol{\text{sum of each pair of opposite angles is } 180^\circ}\) (or "base angles are supplementary" or "it is an isosceles trapezoid" - depending on drop - down options, but from angle check, opposite angles sum to \(180^\circ\) which is the condition for a cyclic quadrilateral).