Question

Namaste! ♡

The "heart" shown in the diagram is formed from an

equilateral triangle ABC and two congruent semicircles on

AB. The two semicircles meet at the point P. The point O

is the centre of one of the semicircles. On the semicircle

with centre O, lies a point X. The lines XO and XP are extended to meet AC at Y and Z respectively.The lines XY and X Z are of equal length.

What is ∠ZXY?

A → 20° B → 25°
C → 30° D →40°

E → 45°

All the best.
Enjoy xD

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Answer 1

$\large{\underline{\underline{\mathfrak{\red{\sf{Answer-}}}}}}$

$\large{\underline{\boxed{\mathfrak{\green{\sf{∠ZXY=20°}}}}}}$

Option A is correct.

$\large{\underline{\underline{\mathfrak{\red{\sf{Explanation-}}}}}}$

$\orange{\boxed{\pink{\underline{\red{\mathfrak{Given-}}}}}}$

The "heart" shown in the diagram is formed from an equilateral triangle ABC and two congruent semicircles on AB. The two semicircles meet at the point P. The point O is the centre of one of the semicircles. On the semicircle with centre O, lies a point X. The lines XO and XP are extended to meet AC at Y and Z respectively.The lines XY and X Z are of equal length.

$\orange{\boxed{\pink{\underline{\red{\mathfrak{To\:find-}}}}}}$

• Value of ∠ZXY

$\orange{\boxed{\pink{\underline{\red{\mathfrak{Solution-}}}}}}$

Let's suppose ∠ZXY = x°

We can say that ∆POX is an isosceles as OP = OX ( radii of same circle )

$\therefore$ ∠OPX = ∠OXP = x°

Also, ∠APZ = ∠OPX ( vertically opposite angles )

So, ∠APZ = x°

It is given that, ∆ABC is an equilateral ∆,

$\implies$ ∠ZAP = 60°

We know that, the exterior angle of a ∆ is equal to the sum of interior opposite angles.

$\implies$ ∠YZX = ∠ZAP + ∠APZ

$\implies$ ∠YZX = ( 60 + x )°

It is also given that, XY = XZ

So, we can say that ∆XYZ is an isosceles ∆.

$\therefore$ ∠ZYX = ∠YZX = ( 60 + x )°

___________________

By using angle sum property in ∆XYZ,

$\implies$ $\tt{x°+(60+x)°+(60+x)°=180°}$

$\implies$ $\tt{3x+120°=180°}$

$\implies$ $\tt{3x=180°-120°}$

$\implies$ $\tt{3x=60°}$

$\implies$ $\tt{x={\cancel\dfrac{60°}{3}}}$

$\implies$ $\tt{x=20°}$

$\large{\underline{\boxed{\mathfrak{\green{\sf{∠ZXY=20°}}}}}}$

Hence option A) is the correct answer.

______________________

#answerwithquality

#BAL

Answer 2

Step-by-step explanation:

a) = 20 is correct answer