Question

EFGH is a parallelogram. Find x y and z Also, state the properties you use to find them ​

Answer 1

Given -

ABCD and EFGH are parallelograms such that ∠A= 120° and ∠G= 70°

To find-

The value of x

Solution -

In parallelogram ABCD,

∠A= ∠C [Opposite angles of a parallelogram are equal] ........1)

And,

∠B= ∠D[Opposite angles of a parallelogram are equal]........2)

Now,

In parallelogram ABCD,

=> ∠A + ∠B + ∠C + ∠D= 360°[Angle sum property of a quadrilateral is 360°]

=> ∠A+ ∠B+ ∠A+ ∠D=360° [by 1) and 2)]

=> 2( ∠A+ ∠B) =360°

=> ∠A+ ∠B= 360°/2

=> 120°+ ∠B=180°

=> ∠B= 180°-120°

=> ∠B= 60°.......3)

Again,

∠G= ∠E=70°[Opposite angles of a parallelogram are equal]........ 4)

Now,

In triangle EPB,

∠E+ ∠P+ ∠B=180°[Angle sum property of triangle is 180°]

=>70°+ x+60°=180°[by 3) and 4)]

=> 130°+x=180°

=> x=180°-130°

=> x =50°

$\boxed{\boxed{{\bf \: \therefore \: The \: value \: of \: x \: is \: {50}^{0} }}}$