Question

two opposite angles of a parallelogram are
$(3x - 2)$
degree and
$(50 - x)$
degree . find the measure of each angle of the parallelogram.

Answer 1

here is your solution

Given:-

Two opposite angles of a parallelogram are (3x − 2)º and (50 − x)º 

We know that opposite angles of a parallelogram are equal•

Hence ,

=>(3x − 2) = (50 − x) 
=> 3x + x = 50 + 2 
=>4x = 52
=>x = 13 

Now

=(3x − 2)º
= 3×(13) − 2)º
= (39 − 2)º
= 37º

Sum of adjacent angles is 180º

Hence,

Other two equal opposite angles.
= 180º − 37º = 143°

The measure of each angle of the parallelogram are 37° ,143°,37°,143°.

hope it helps you

Answer 2

given, two opposite Angles are

( 3 x - 2 )° and ( 50 - x )°

since , we know that opposite sides of parallelogram are congruent , therefore there opposite angles will also be congruent (equal )

so now , according to question ,

angle ( 3 x - 2 )° is congruent to angle ( 50 - x )

3 x - 2 = 50 - x => 3x + x = 50 + 2

=> 4 x = 52 = > x = 13

so now measure of given two opposite angles are ,

3 x - 2 = 3 ( 13 ) - 2 = 39 - 2 = 37°

50 - x = 50 - 13 = 37°

thus ,each of these two equal and opposite angles' measure = 37 °

since ,we know that consecutive angles are supplementary ,

let the two consecutive supplementary angles are , 37 °, x

sum of supplementary angles = 180

37 ° + x = 180°

x = 180° - 37 ° = 143°

so now ,measure of other two equal and opposite angles = 143°

therefore ,measure of each angles of

parallelogram are = 37° , 143° , 37° , 143°

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Your Answer : 37° , 143° , 37° , 143°
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