In parallelogram ABCD, angle $a = 2x + 25$ and angle $b= 3x -5$ so find all the angles.

Given: In parallelogram ABCD, angle $a = 2x + 25$ and angle $b= 3x -5$.

To do:  Find all angles

Answer:

In a parallelogram, adjacent angles are supplementary.

Angle A and angle B are adjacent angles and hence are supplementary.

$A + B = 2x + 25 + 3x -5 = 180°$

$5x + 20 = 180;  5x = 180 - 20 = 160$

$x = \frac{160}{5} = 32°$.

So angle $A = 2x + 25 = 2(32) + 25 = 64 + 25 = 89°$

So angle $B = 3x - 5 = 3(32) - 5 = 96 - 5 = 91°$

So $A = 89°$ and $B = 91°$

Since opposite angles of a parallelogram are equal

∠A = ∠C = 89° and ∠B = ∠D = 91°

So the angles the parallelogram are ∠A =89°; ∠B = 91°, ∠C = 89°; ∠D = 91°

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Updated on: 10-Oct-2022

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