Answer :
sum of adjacent angles =180
=> 4x-15+5x-3=180
=>9x-18=180
=>9x=198
=>x=22
opposite angles are equal
therefore angles are 73,107,73,107
=> 4x-15+5x-3=180
=>9x-18=180
=>9x=198
=>x=22
opposite angles are equal
therefore angles are 73,107,73,107
All angles of parallelogram measure 73°, 73°, 107° and 107°.
Given - Adjacent angles of parallelogram
Find - All angles of parallelogram
Solution - The sum of adjacent angles of parallelogram is 180°. So, representing given information as equation -
[tex]4x - 15 + 5x - 3 = 180[/tex]
Performing addition and subtraction
[tex]9x - 18 = 180[/tex]
[tex]9x = 180 + 18[/tex]
Performing addition
[tex]9x = 198[/tex]
[tex]x = \frac{198}{9} [/tex]
Performing division
x = 22
The adjacent angles of parallelogram= (4*22-15) and (5*22-3).
Adjacent angles = (88-15) and (110-3)
Adjacent angles = 73 and 107
As per the known fact, the opposite angles of parallelogram are equal.
So, all the angles of parallelogram are 73°, 73°, 107° and 107°.
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