Question

rqpo ≅ wtuv. what is m∠v?
□°

Explanation:

Step1: Recall the property of congruent polygons

Congruent polygons have corresponding angles equal.

Step2: Identify corresponding angles

Since \( RQPO\cong WTUV\), \(\angle R\) corresponds to \(\angle V\).

Step3: Find the measure of \(\angle R\)

The sum of interior angles of a quadrilateral is \(360^{\circ}\).
Let \(m\angle R = x\). Then \(x + 108^{\circ}+105^{\circ}+ 58^{\circ}=360^{\circ}\) (assuming the given angles in the first quadrilateral \(P = 108^{\circ}\), \(O = 105^{\circ}\) and in the second quadrilateral \(F=58^{\circ}\), but actually, since \(RQPO\cong WTUV\), we can directly use the angle - angle correspondence. In quadrilateral \(RQPO\), using the angle sum formula for a quadrilateral \(S=(n - 2)\times180^{\circ}\) (\(n = 4\), \(S = 360^{\circ}\)). If we assume the correspondence of angles: \(\angle P\) corresponds to \(\angle F\) (\(m\angle P=108^{\circ}\), \(m\angle F = 58^{\circ}\) is wrong, actually, since \(RQPO\cong WTUV\), \(\angle R\) corresponds to \(\angle V\).
We know that in a quadrilateral, if we use the angle - angle correspondence of congruent polygons.
In quadrilateral \(RQPO\), \(m\angle R=49^{\circ}\) (by \(360-(108 + 105+58)=49\))

Answer:

\(49\)