Question

In a parallelogram KLMN angle 1 point
L = xº and LM = (3x+20°) find xº
measure of angle K and
measure of angle N
O 140,960,52°
O 28°,720,108°
O 420,138°,42°
O 400,1409,40°​

Answer 1

Answer :-

• The value of x is 40.
• The measure of ∠N is 40°.
• The measure of ∠K is 140°.

[ Option. d. 40°, 140°, 40° ] is the correct option.

Step-by-step explanation:

To Find :-

• The value of x
• The measure of ∠L
• The measure of ∠N

Solution:

Given that,

• ∠L = x°
• ∠M = ( 3x + 20 )°

As ∠L and ∠M are forming adjacent angles of parallelogram, Therefore,

• ∠L + ∠M = 180°
• x° + ( 3x + 20 )° = 180°

=> x + ( 3x + 20 ) = 180

=> x + 3x + 20 = 180

=> 4x + 20 = 180

=> 4x = 180 - 20

=> 4x = 160

=> x = 160/4

=> x = 40

The value of x is 40.

Now, The measure of ∠L and ∠M are:

• ∠L [ given, ∠L = x ]

=> x

=> 40°

• ∠M [ given, ∠M = ( 3x + 20 ) ]

=> ( 3x + 20 )

=> ( 3*40 + 20 )

=> ( 120 + 20 )

=> 140°

Therefore, The measure of ∠L and ∠M is 40° and 140° respectively.

According the question,

As we know that,

Opposite angles of parallelogram are equal. So,

• ∠L = ∠N
• ∠M = ∠K

Hence,

• The measure of ∠N is 40°
• The measure of ∠K is 140°.