Question

Question=>
The given figure is a parallelogram. Find x,y and z.​

Answer 1

As per the given information in the question, we have:

• EHOP is a parallelogram.
• ∠EHP = 40°

We have been asked to find the value of x, y and z.

We know:

• If two parallel lines cut by a transversal, then the alternate interior angles are equal.

Using this property:

$\longrightarrow\: \: \: \: \:\sf{\angle OPH=\angle EHP}$

Here, value of ∠EHP is 40° and ∠OPH is y, so equating the values, we get:

$\longrightarrow\: \: \: \: \:\bold{y={40}^{\circ}}$

We know:

• In triangle, sum of two opposite interior angles is equal to the exterior angle.

Using this property:

$\longrightarrow\: \: \: \: \:\sf{\angle PHO+\angle HPO= Exterior\: angle}$

Here, exterior angle is 70° and angle HPO is 40°, so equating the values, we get:

$\longrightarrow\: \: \: \: \:\sf{\angle PHO+40=70}$

Transposing 40 from LHS to RHS,

$\longrightarrow\: \: \: \: \:\sf{\angle PHO=70-40}$

Performing subtraction.

$\longrightarrow\: \: \: \: \:\sf{\angle PHO=30}$

Substituting value of ∠PHO as z.

$\longrightarrow\: \: \: \: \:\bold{z={30}^{\circ}}$

We know:

• Sum of adjacent angles in a parallelogram equals to 180°.

Using this property:

$\longrightarrow\: \: \: \: \:\sf{\angle FEG+\angle EGH=180}$

Here, ∠EGH=∠EGF+∠FGH. So,

$\longrightarrow\: \: \: \: \:\sf{\angle FEG+\angle EGF+\angle FGH=180}$

Equating all the values, we get:

$\longrightarrow\: \: \: \: \:\sf{x+40+30=180}$

Performing addition.

$\longrightarrow\: \: \: \: \:\sf{x+70=180}$

Transposing 70 from LHS to RHS,

$\longrightarrow\: \: \: \: \:\sf{x=180-70}$

Performing subtraction.

$\longrightarrow\: \: \: \: \:\bold{x={110}^{\circ}}$

❝ Therefore, value of x is 110°, y is 40° and z is 30°. ❞