Question

please help me!!!!!!!!!​

Answer 1

Step-by-step explanation:

Solution :-

1)

In a ABCD paralellogram,

< A = 125°

< D= x°

We know that

The adjacent angles are supplementary in a Parallelogram

=> <A+<D = 180°

=> 125°+x° = 180°

=> x° = 180°-125°

=> x° = 55°

and

We know that

Opposite angles are equal in a Parallelogram

=> <A = <C

=> 125° = y+56°

=>y = 125°-56°

=>y = 69°

and < A + < B = 180°

=> 125°+< B = 180°

=> < B = 180°-125°

=>< B = 55°

Now ,z is the exterior angle of ∆ECB

We know that

The exterior angle is equal to the sum of the opposite interior angles

=> z = 55°+56°

=>z = 111°

(or)

and from ADCE Trapezium

We know that

The adjacent interior angles in a trapezium sum up to be 180°.

=> <C+<E = 180°

=> y+z = 180°

=>z = 180°-y

=> z = 180°-69°

=> z = 111°

The value of x = 55° , y = 69° , z =111°

2)

Given that

In a ABCD paralellogram,

< A = 3y

<B = 2y-5

We know that

The adjacent angles are supplementary in a Parallelogram

=> <A+<B = 180°

=> 3y+2y-5 = 180°

=> 5y-5 = 180°

=> 5y = 180+5

=> 5y = 185

=> y = 185/5

=> y = 37°

and

< B and < C are Adjacent angles

We know that

The adjacent angles are supplementary in a Parallelogram

=> <B +<C= 180°

So, < B = 2y-5

=> <B = 2(37°)-5

=> < B = 74°-5°

=><B = 69°

=> 69°+3x+3 = 180°

=> 3x+72°= 180°

=> 3x = 180-72°

=> 3x = 108°

=> x = 108°/3

=> x = 36°

Therefore, x = 36° and y = 37°

Used formulae:-

• The adjacent angles are supplementary in a Parallelogram
• The adjacent interior angles in a trapezium sum up to be 180°.
• Opposite angles are equal in a Parallelogram
• The exterior angle is equal to the sum of the opposite interior angles