Question

two adjacent angles of a parallelogram are in the ratio 4:5 . Find the measure of all the angles

Answer 1

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$<B><I>HERE IS YOUR ANSWER :-$


Let the angles be 4x° and 5x°.


We know that adjacent angles of parallelogram are supplementary. i. e. their sum is 180°.


4x + 5x = 180.


=> 9x = 180


=> x = 180/9


=> x = 20 .


4x = 4 × 20 = 80°


5x = 5 × 20 = 100°


So the measures of all angles are 80° , 100° , 80° and 100°.


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Answer 2

The measures of adjacent angles of parallelogram add upto 180°. It means ghey are supplementary.

____________________

Given, two adjacent angles of a parallelogram are in the ratio 4 : 5

So, let the angles be 4x and 5x

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Solution :-

According to the question,

4x + 5x = 180

9x = 180

x = $\dfrac{180}{9}$

x = 20

____________________

1st adjacent angle's measure is 4x

=> 4 × 20

=> 80°

2nd adjacent angle's measure is 5x

=> 5 × 20

=> 100°

___________________

We know that adjacent angles of parallelogram are congruent.


$\therefore{}$ The measure of four adjacent angles of parallelogram are 80°, 100°, 80°, 100° respectively.