Question

In the following, figure, if ABIICD, angle APQ=64 degree and angle PRD = 125 degree, find the value of x and y​

Answer 1

★ Solution :

In the figure attached in the answer, we had marked other two angles namely a. The other angle at the top of the diagram is marked with 125°, which isn't given in the figure attached in the question. It's marked as 125° because, the corresponding angles are always same. With the help of that angle, we can find the value of y. But, first we'll find the value of ∠a.

Value of ∠a :-

$\sf \leadsto Straight \: line \: angle = {180}^{\circ}$

$\sf \leadsto {125}^{\circ} + \angle{a} = {180}^{\circ}$

$\sf \leadsto \angle{a} = 180 - 125$

$\sf \leadsto \angle{a} = 180 - 125$

$\sf \leadsto \angle{a} = {55}^{\circ}$

Now, let's find the value of the ∠y. To find the value of that angle, we use the same concept which we used to find the value of the ∠a i.e, the straight line angle always measures as 180°. So, let's find out the value of the ∠y with the same concept

Value of ∠y :-

$\sf \leadsto Straight \: line \: angle = {180}^{\circ}$

$\sf \leadsto {64}^{\circ} + \angle{y} + {55}^{\circ} = {180}^{\circ}$

$\sf \leadsto {119}^{\circ} + \angle{y} = {180}^{\circ}$

$\sf \leadsto \angle{y} = 180 - 119$

$\sf \leadsto \angle{y} = {61}^{\circ}$

Now, let's find the value of ∠x. To find the value of this angle, we use different concept. This concept is applicable only for the triangles. This concept says us that, the sum of all the angels in any triangle always equals to 180°. So, let's find out the value of ∠x through this concept.

Value of ∠x :-

$\sf \leadsto {Angle \: sum \: property}_{(Triangle)} = {180}^{\circ}$

$\sf \leadsto {61}^{\circ} + {55}^{\circ} + \angle{x} = {180}^{\circ}$

$\sf \leadsto \angle{116}^{\circ} + \angle{x} = {180}^{\circ}$

$\sf \leadsto \angle{x} = 180 - 116$

$\sf \leadsto \angle{x} = {64}^{\circ}$

Therefore, the value of the ∠x and ∠y are 64° and 61° respectively.

Answer 2

Given that : In the following, figure, if AB II CD, angle APQ = 64° and angle PRD = 125°

Need To FinD : find the value of ∠x ,∠y.

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⠀⠀⠀⠀⠀_________________________

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❍ let's start finding the ∠x and ∠y By solving further.

» For Clearly understanding of this solutions Kindly refer to the given attachment Diagram !

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$\underline{\bigstar\:\boldsymbol{ According \: To \: Question \::}}$

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» It is rule that sum of all angles in ∆Triangle is equal to 180° .

» It means if we add all three angles of triangle it will be equal to 180°

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$\quad\footnotesize\bf{\red{\dag}\:\underline{\boxed{\pink{\frak{Calculating \: Value \: Of Angle \;A \; :}}}}}$

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$\qquad$$\blue\maltese$Straight line angle is 180°

$\qquad$$\green\twoheadrightarrow$125° + ∠a = 180°

$\qquad$$\green\twoheadrightarrow$∠a = 180° - 125 °

$\qquad$$\green\twoheadrightarrow$∠a = 55°

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$\quad\footnotesize\bf{\red{\dag}\:\underline{\boxed{\green{\frak{Calculating \: Value \: Of Angle \;y \; :}}}}}$

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$\qquad$$\orange\maltese$Straight line angle is 180°

$\qquad$$\blue\twoheadrightarrow$∠64° + ∠y + ∠a = 180°

$\qquad$$\blue\twoheadrightarrow$64° + 55° + ∠y = 180°

$\qquad$$\blue\twoheadrightarrow$∠y = 180° - 119°

$\qquad$$\blue\twoheadrightarrow$∠y = 61°

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⠀⠀⠀⠀⠀_________________________

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$\quad\footnotesize\bf{\red{\dag}\:\underline{\boxed{\orange{\frak{Calculating \: Value \: Of Angle \;x \; :}}}}}$

$\qquad$$\purple\maltese$Angle Sum Property of (∆) 180°

$\qquad$$\red\twoheadrightarrow$∠y + ∠a + ∠x = 180°

$\qquad$$\red\twoheadrightarrow$61° + 55° + ∠x = 180°

$\qquad$$\red\twoheadrightarrow$∠x = 180° - 116°

$\qquad$$\red\twoheadrightarrow$∠x = 64°

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$\pink\dag$Therefore :

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$\underline{ \sf \pmb{ Measurements \; Of \; All \; Angles }} \red \bigstar$

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$:\red\longmapsto$Value of angle ∠x = 64°

$:\pink\longmapsto$Value of angle ∠y = 61°

$:\blue\longmapsto$Value of angle ∠a = 55°

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