Question

In the given figure, ABCD is a parallelogram. Find x, y and z.
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Answer 1

Step-by-step explanation:

Given:-

ABCD is a Parallelogram

angle A = 125°

angle D = x°

angle DCE = y°

angle BCE = 56°

angle CEA = z°

To find :-

Find the value of x ,y and z ?

Solution :-

Given that :-

ABCD is a Parallelogram

angle A = 125°

angle D = x°

We know that

Adjacent angles are supplementary in a Parallelogram

=> angle A + angle D = 180°

=>125°+x° = 180°

=> x° = 180°-125°

=> x° = 55°

So, angle D = 55°

We know that

Opposite angles are equal in a Parallelogram

Given that

angle D = angle B = 55°

angle DCE = y°

angle BCE = 56°

We know that

Opposite angles are equal in a Parallelogram

=> angle A = angle C

=> 125° = angle DCE+ angle BCE

=> 125° = y+56°

=> y = 125°-56°

=> y = 69°

angle CEA = z°

In ∆ CBE ,

The side EB is extended to A then

We know that

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

=> z = angle B + BCE

=> z = 55°+56°

=>z = 111°

or

In a Parallelogram opposite sides are parallel

AB and CD are parallel lines and CE is a transversal then

y and z are interior angles on the same side to the transversal

They are Supplementary

=> y+z = 180°

=> 69°+z = 180°

=> z = 180°-69°

=> z = 111°

Answer:-

x = 55°

y = 69°

z = 111°

Used formulae:-

• In a Parallelogram opposite sides are parallel
• The exterior angle is equal to the sum of two opposite interior angles
• Opposite angles are equal in a Parallelogram
• Adjacent angles are supplementary in a Parallelogram.