Question

Two adjacent angle of a pallelogram are (4x- 15) and (5x-3) . Find the measure of all angles of the parallelogram.

Answer 1

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

Answer 2

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 -

$4x - 15 + 5x - 3 = 180$

Performing addition and subtraction

$9x - 18 = 180$

$9x = 180 + 18$

Performing addition

$9x = 198$

$x = \frac{198}{9}$

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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