Question

The consecutive interior angle of a parallelogram ABCD are angle A = (2X+4)degree , B( Y+3) degree angle C (4x -5) , D = (2Y+10) degree find the value of X​

Answer 1

Step-by-step explanation:

Given :-

The consecutive interior angle of a parallelogram ABCD are angle A = (2X+4)°, angle B=( Y+3)° ,

angle C = (4x -5)° , D = (2Y+10)°.

To find :-

Find the value of X ?

Solution :-

Given that

ABCD is a Parallelogram

The consecutive interior angles are A,B,C,D

angle A = (2X+4)°

angle B = (Y+3)°

angle C = (4X-5)°

angle D = (2Y+10)°

We know that

Opposite angles are equal in a Parallelogram

angle A = angle C

=> (2X+4)° = (4X-5)°

=> 2X°+4° = 4X°-5°

=> 4°+5° = 4X° -2X°

=> 9° = 2X°

=> 2X° = 9°

=> X° = 9/2° or 4.5°

and

angle B = angle D

=> Y+3° = 2Y+10°

=> 2Y°-Y° = 10°-3°

=> Y° = 7°

Therefore, X° = 4.5° and Y° = 7°

Answer:-

The value of X for the given problem is

9/2° or 4.5°

Used formulae:-

• In a Parallelogram, Opposite angles are equal.

Points to know:-

• In a Parallelogram, Opposite sides are parallel and equal.

• Adjacent angles are supplementary.