∠MNV and ∠NMR are congruent to each other because the trapezoid is isosceles. ∠NVR and ∠MRV are also congruent to each other. The sum of interior angles of a trapezoid is 360°. See trapezoid MNRV. ∠MNV + ∠NMR + ∠NVR + ∠MRV = 360° 116° + 116° + ∠NVR + ∠MRV = 360° 232° + 2(∠MRV) = 360° 2(∠MRV) = 360° - 232° 2(∠MRV) = 128° ∠MRV = 64°
∠SRV = ∠MRV = 64° The measure of angle SRV is 64 degrees