Question

find ( mangle r ) in parallelogram ( pqrs ).
( mangle r = square^circ )

Explanation:

Step1: Recall parallelogram angle property

In a parallelogram, consecutive angles are supplementary (sum to \(180^\circ\)). So, \(\angle R + \angle Q = 180^\circ\). Substitute the given expressions: \((5a - 31) + (a + 37) = 180\).

Step2: Solve for \(a\)

Simplify the equation: \(5a - 31 + a + 37 = 180\) → \(6a + 6 = 180\) → \(6a = 174\) → \(a = 29\).

Step3: Find \(m\angle R\)

Substitute \(a = 29\) into \(5a - 31\): \(5(29) - 31 = 145 - 31 = 114\).

Answer:

\(114\)