The sum of the angles in a trapezoid is 360 degrees. Since MN || RV, we know that ∠MNV and ∠RVS are alternate interior angles, making them congruent. This means ∠RNVS is 180° - ∠MNV - ∠RVS = 180° - ∠MNV - ∠MNV.
But since RSTV is an isosceles trapezoid, we know that ∠MNV and ∠SNV are congruent, and ∠RVS and ∠RUT are congruent (U is the intersection of MN and RV). This means ∠RNVS = 180° - ∠RVS - ∠RVS = 180° - 2∠RVS.
We know that ∠RNVS is also ∠RNV + ∠SNV. Since RSTV is an isosceles trapezoid, we also know that ∠RNV = ∠SNV.
Therefore, we have ∠RNV + ∠SNV = 180° - 2∠RVS. Since ∠RNV = ∠SNV, this simplifies to 2∠RNV = 180° - 2∠RVS.
Dividing both sides of the equation by 2, we get ∠RNV = 90° - ∠RVS. Since RSTV is an isosceles trapezoid, we know that ∠RVS = ∠TSR, making ∠RNV = 90° - ∠TSR.
But in an isosceles trapezoid, ∠TSR = ∠SRV. Therefore, we have ∠SRV = 90° - ∠SRV.
Adding ∠SRV to both sides, we get 2∠SRV = 90°.
Dividing both sides by 2, we get ∠SRV = 45°.
Therefore, the answer is: the m∠SRV is 45°.
RSTV is an isosceles trapezoid with bases RV and ST and MN || RV. Find the m∠SRV.
• 180°
120°
• 64°
• 60°
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