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Opposite Sides of a Parallelogram Are Equal

In a parallel...

Question

In a parallelogram ABCD, If $∠$ A = ${(3 x + 2)}^{°}$ , $∠$ B = ${(2 x - 32)}^{°}$ then find the value of x and then find the measures of $∠$ C and $∠$ D.

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Solution

Interior angles on the same side of the transversal are supplementary.
$∠$ A + $∠$ B = 180 $°$
$\Rightarrow$ ${(3 x + 12)}^{°}$ + ${(2 x - 32)}^{°}$ = 180 $°$
$\Rightarrow 5 x - 20 = 180 ° \Rightarrow 5 x = 200 \Rightarrow x = 40 °$
Thus, $∠$ A = $3 \times 40 ° + 12 = 132 °$
$∠ B = 2 x - 32 = 2 \times 40 ° - 32 = 48 °$
Also, opposite angles of a parallelogram are congruent.
$∠ A = ∠ C = 132 ° ∠ B = ∠ D = 48 °$

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