In a parallelogram ABCD, $∠$ A =x $°$ , $∠$ B = 3x +20 $°$ , find x and find $∠$ C and $∠$ D.

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Solution

In parallelogram ABCD, $∠$ A and $∠$ B are adjacent angles supplementary to each other.

Thus, we have:
$∠$ A + $∠$ B = 180°
Also,
$∠$ A = x° and $∠$ B = (3x + 20)°
$\Rightarrow$ x° + 3x° + 20° = 180°
$\Rightarrow$ 4x° + 20° = 180°
$\Rightarrow$ 4x° = 160°
$\Rightarrow$ x° = 40°
$\Rightarrow$ x = 40
We know that opposite angles of a parallelogram are congruent.
Thus, we have:
$∠$ C = $∠$ A = x°
$\Rightarrow$ $∠$ C= 40°
$∠$ D = $∠$ B
$\Rightarrow$ $∠$ D = 3x° + 20°
= 3(40°) + 20°
= 120° + 20°
= 140°
$∴ ∠ D = 140 °$

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