In parallelogram PQRS, m∠Q = 130°. Find the measure of the other angles of □PQRS.

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Solution

For parallelogram PQRS, m $∠$ Q = 130°.
m $∠$ Q = m $∠$ S (Opposite angles of a parallelogram are congruent)
m $∠$ S = 130°
m $∠$ Q + m $∠$ R = 180° (Sum of adjacent angles of a parallelogram is 180°, as they are on the same side of the transversal.)
m $∠$ R = 180° – 130° = 50°
m $∠$ P = m $∠$ R = 50° (Opposite angles of a parallelogram are congruent)
m $∠$ S = 130°
m $∠$ R = m $∠$ P = 50°

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