Question

If corresponding angles of a parallelogram are in the ratio 1:5 then find all its angles

Answer 1

Finding the Angles of parallelogram

Answer: four angles of parallelogram are 30° , 150° , 30° and 150°.

Explanation:

Given that corresponding angles of parallelogram are in ration 1:5. Assuming that it menas consecutive angles of parallelogram.

lets assume four angles of parallelogram are ∠1 ,∠2 ,∠3 and ∠4.

lets consider that ∠1 and ∠2 are corresponding angles . And ∠3 is opposite to ∠ 1 and ∠ 4 is opposite to ∠2.

As consecutive angles are in ratio 1 : 5 , lets assume ∠ 1 = 1x and ∠2 = 5x.

AS CONSECUTIVE ANGLES OF PARALLELOGRAM ARE SUPPLEMENTARY

=> ∠ 1 + ∠2 = 180°

=> 1x + 5x = 180°

=> 6x = 180°

=> x = 180/6 = 30

so ∠1 = 1x = 1 × 30 = 30°

and ∠2 = 5x = 5×30 = 150°

Now we have two consecutive angles as 30° and 150°.

Also OPPOSITE ANGLES OF PARALLELOGRAM ARE EQUAL.

=> ∠3 = ∠1 = 30° and ∠2 = ∠4 = 150°.

Hence four angles of parallelogram are 30° , 150° , 30° and 150°.

#answerwithquality

#BAL