Question

what are the missing angle measures in parallelogram rstu?

○ ( mangle r = 70^{circ}, mangle t = 110^{circ}, mangle u = 110^{circ} )
○ ( mangle r = 110^{circ}, mangle t = 110^{circ}, mangle u = 70^{circ} )
○ ( mangle r = 110^{circ}, mangle t = 70^{circ}, mangle u = 110^{circ} )
○ ( mangle r = 70^{circ}, mangle t = 110^{circ}, mangle u = 70^{circ} )

Explanation:

Step1: Use the property of opposite angles in a parallelogram

In a parallelogram, opposite angles are equal. So, \(m\angle U=m\angle S = 70^{\circ}\)

Step2: Use the property of consecutive angles in a parallelogram

Consecutive angles in a parallelogram are supplementary (\(m\angle R + m\angle S=180^{\circ}\)). Given \(m\angle S = 70^{\circ}\), then \(m\angle R=180^{\circ}- 70^{\circ}=110^{\circ}\)

Step3: Use the property of opposite angles again

Since \(m\angle T=m\angle R\) (opposite angles of a parallelogram), \(m\angle T = 110^{\circ}\)

Answer:

\(m\angle R = 110^{\circ},m\angle T = 110^{\circ},m\angle U = 70^{\circ}\) (the second option)