Question

2. In a parallelogram ABCD, if LA = (3x + 12),
B = (2x - 32)º, then find the value of x and then
find the measures of LC and LD.​

Answer 1

Step-by-step explanation:

Given:-

In a parallelogram ABCD, LA = (3x + 12),

LB = (2x - 32)º.

To find:-

Find the value of x and then ,find the measures of LC and LD.

Solution:-

Given that

In a parallelogram ABCD,

LA = (3x + 12)°

LB = (2x - 32)º.

It is clear that angle A and angle B are adjacent angles .

We know that

In a Parallelogram, Adjacent angles are supplementary.i.e. The sum of two adajacent angles in a Parallelogram is 180°

=> angle A+angle B = 180°

=> (3X+12)°+(2X-32)°=180°

=> 3X°+12°+2X°-32°=180°

=> (3X°+2X°)+(12°-32°) = 180°

=> (5X°)+(-20°)= 180°

=> 5X°-20°=180°

=> 5X°=180°+20°

=>5X°=200°

=>X°=200°/5

=>X°=40°

The value of X = 40°

Now , angle A = (3X+12)°

=> (3×40°+12°

=>120°+12°

=>132°

and angle B = 2X°-32°

=>2×40°-32°

=> 80°-32°

=> 48°

(or)

angle B = 180°-angle A

=> angle B=180°-132°

Angle B = 48°

we know that

The opposite angles are equal in a Parallelogram

angle A = angle C = 132°

angle B= angle D = 48°

Answer:-

The value of X= 40°

Angle C = 132°

Angle D=48°

Used formulae:-

• In a Parallelogram, Adjacent angles are supplementary.i.e. The sum of two adajacent angles in a Parallelogram is 180°
• The opposite angles are equal in a Parallelogram.