Question

in a parallel diagram ABCD , if angle A=3x+12degree angle B =2x-12degree then find the value of x and then find the measure of angle C and angle D​

Answer 1

Step-by-step explanation:

Given:-

In a parallel diagram ABCD , angle A=(3x+12)° angle B =(2x-12)° .

To find:-

Find the value of x and then find the measure of angle C and angle D ?

Solution:-

Given that :-

In a parallel diagram ABCD , ∠ A=(3x+12)° ∠ B =(2x-12)° .

angle A and angle B are Adjacent angles in the Parallelogram ABCD

We know that

The sum of two adjacent angles in a Parallelogram is 180°

=> ∠ A + ∠ B = 180°

=> (3x+12)°+(2x-12)°=180°

=> (3x+2x)°+(12°-12°) = 180°

=> 5x°+0° = 180°

=>5x°=180°

=>x°=180°/5

=>x°=36°

The value of x = 36°

Now ,

∠ A = 3x°+12°

=3(36°)+12°

=108°+12°

=120°

and ∠A+∠B=180°

=>120°+ ∠B = 180°

=> ∠ B = 180°-120°

∠ B = 60°

We know that

Opposite angles are equal in a triangle

∠ A = ∠ C = 120°

∠B = ∠D = 60°

Answer:-

Value of x° = 36°

The measurement of ∠ A = 120°

The measurement of ∠ B = 60°

The measurement of ∠ C = 120°

The measurement of ∠ D = 60°

Used formulae:-

In a Parallelogram,

• Adjacent angles are Supplementary.

• Opposite angles are equal

Answer 2

Answer:

. ABCD is a parallelogram. [Given] ∴ ∠A + ∠B = 180° [Adjacent angles of a parallelogram are supplementary], ∴ (3x + 12)° + (2x-32)° = 180° ∴ 3x + 12 + 2x – 32 = 180 ∴ 5x – 20 = 180 ∴ 5x = 180 + 20 ∴ 5x = 200 ∴ x = 200/5 ∴ x = 40 ii. ∠A = (3x + 12)° = [3(40) + 12]° = (120 + 12)° = 132° ∠B = (2x – 32)° = [2(40) – 32]° = (80 – 32)° = 48° ∴ ∠C = ∠A = 132° ∠D = ∠B = 48° [Opposite angles of a parallelogram] ∴ The value of x is 40, and the measures of ∠C and ∠D are 132° and 48° respectivelyRead more on Sarthaks.com - https://www.sarthaks.com/849948/in-parallelogram-abcd-if-a-3x-12-b-2x-32-then-liptl-the-value-of-and-the-measures-of-c-and-d