Question

find each measure.

1. m∠a
2. m∠r

Explanation:

Step1: Identify the shape type

The first figure ABCD is a parallelogram. In a parallelogram, opposite - angles are equal and adjacent - angles are supplementary.

Step2: Find \(m\angle A\)

Since \(\angle A\) and \(\angle D\) are adjacent angles in parallelogram \(ABCD\), and the sum of adjacent angles in a parallelogram is \(180^{\circ}\). Given \(m\angle D = 82^{\circ}\), then \(m\angle A=180 - 82\).
\(m\angle A = 98^{\circ}\)

For the second figure \(QRST\), it is an isosceles trapezoid. In an isosceles trapezoid, base - angles are equal and adjacent - angles along a non - parallel side are supplementary.

Step3: Identify the angle relationship

\(\angle R\) and \(\angle T\) are adjacent angles along a non - parallel side.

Step4: Find \(m\angle R\)

Since \(\angle R\) and \(\angle T\) are supplementary and \(m\angle T = 105^{\circ}\), then \(m\angle R=180 - 105\).
\(m\angle R = 75^{\circ}\)

Answer:

1. \(m\angle A = 98^{\circ}\)
2. \(m\angle R = 75^{\circ}\)