Question

Given PQRS is a parallelogram, solve for x and y. Then solve for m

Answer 1

see explanation

Explanation:

The opposite sides of a parallelogram are congruent, then

19x - 9 = 13x + 15 ( subtract 13x from both sides )

6x - 9 = 15 ( add 9 to both sides )

6x = 24 ( divide both sides by 6 )

x = 4

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Consecutive angles are supplementary, sum to 180° , that is

10y - 37 + 4y + 7 = 180

14y - 30 = 180 ( add 30 to both sides )

14y = 210 ( divide both sides by 14 )

y = 15

Then

∠ R = 10y - 37 = 10(15) - 37 = 150 - 37 = 113°

Then

∠ P = 113° ( opposite angles are congruent )