Question

In a parallelogram ABCD, LA=xº,
LB = (3x + 20°) Find x and LC and LD ​

Answer 1

Correct question:

In a parallelogram ABCD, ∠A = x°, ∠B = (3x+20)°. Then find x and ∠C and ∠D.

__________________

Given:

• ∠A = x°
• ∠B = (3x+20)°

__________________

To find:

• Value of x
• ∠C and ∠D.

__________________

Solution:

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

So,

∠A+∠B = 180°

x° + (3x+20)° = 180°

x° + 3x°+20° = 180°

4x°+20° = 180°

4x° = 180°-20°

4x° = 160

x = $\sf \dfrac {160}{4}$

$\boxed {\mathfrak {\pink {x = 40 \degree}}}$

☆___________☆

Now,

∠A = x° = 40°

∠B = (3x+20)° = (3×40+20)° = 140°

☆___________☆

∠A = ∠C

$\bigstar {\sf {Opposite\ angles\ of\ parallelogram\ are\ equal}}$

∠C = 40°

∠B = ∠D

$\bigstar {\sf {Opposite\ angles\ of\ parallelogram\ are\ equal}}$

∠D = 140°

__________________

Answers:

• Value of x is 40°.
• ∠C is 40° and ∠D is 140°.