# Two Opposite Angles of a Parallelogram Are (3x − 2)° and (50 − X)°. Find the Measure of Each Angle of the Parallelogram. - Mathematics

Two opposite angles of a parallelogram are (3x − 2)° and (50 − x)°. Find the measure of each angle of the parallelogram.

#### Solution

$\text{ Oppostie angles of a parallelogram are congurent } .$
$\therefore \left( 3x - 2 \right)° = \left( 50 - x \right)°$
$3x°- 2° = 50°- x°$
$3x°+ x°= 50° + 2°$
$4x°= 52°$
$x° = 13°$
$\text{ Putting the value of x in one angle }:$
$3x° - 2°= 39°- 2°$
$= 37°$
$\text{ Opposite angles are congurent }:$
$\therefore 50 - x°$
$= 37°$
$\text{ Let the remaining two angles be y and z } .$
$\text{ Angles y and z are congurent because they are also opposite angles } .$
$\therefore y = z$
$\text{ The sum of adjacent angles of a paralle\logram is equal to } 180° .$
$\therefore 37°+ y = 180°$
$y = 180°- 37°$
$y = 143°$
$\text{ So, the anlges measure are }:$
$37°, 37°, 143° \text{ and } 143°$

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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 17 Understanding Shapes-III (Special Types of Quadrilaterals)
Exercise 17.1 | Q 7 | Page 10