Math, asked by rajeshshingankuli, 7 months ago

in figure if AB||CD, CD||EF and y:z= 3:7, find x.​

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Answered by Anonymous
20

  \sf \underline {\orange {\: Given : }}

  • AB\bf \parallel CD and CD\bf \parallel EF
  • The ratio of \bf \angle y and \bf \angle z is 3:7.

  \sf \underline {\orange {To \: find  : }}

  • The unknown \bf \angle x = ?

  \sf \underline {\orange {\: Solution : }}

We know that,

  • Corresponding angles are equal

HERE,

\bf \angle y and \bf \angle z are equal to 180° (linear pair).

So,

  • Let's assume that \bf \angle y and \bf \angle z is 3x and 7x.

According to the question,

 \orange \leadsto \bf \:  \: 3x \:  +  \: 7x = 180  \degree \:  \\  \bf \implies \: 10x \:  = 180 \: \degree \\  \bf \implies \:x  \:  =  \frac{18 \cancel0}{1 \cancel0}  \\  \bf  \red  \dag {\underline{ \boxed{ \bf x \:  = \: 18 \: \degree}}{\red  \dag }}

HENCE,

\bf \angle y = 3x = 3 × 18 =54°

\bf \angle z = 7x = 7 × 18 = 126°

NOW,

We also know that

  • Adjacent angles are equal to 180°

THEREAFTER,

we can write it that :

\bf \angle x and \bf \angle y = 180° ( Adjacent angles are equal to 180°).

Substituting the value of \bf \angle y :

</strong><strong>\</strong><strong>r</strong><strong>e</strong><strong>d</strong><strong> \leadsto  \bf\angle  x \:  +  \:  \angle \:   y = 180° \\ </strong><strong>\</strong><strong>r</strong><strong>e</strong><strong>d</strong><strong> \leadsto \bf \angle x \: +  54 \degree = 180\degree \\  \bf</strong><strong> </strong><strong>\</strong><strong>r</strong><strong>e</strong><strong>d</strong><strong> \leadsto \:  \angle x = (180 - 54)\degree \\   </strong><strong>\</strong><strong>b</strong><strong>f</strong><strong> </strong><strong>\red \dag{ \underline{ \boxed{\bf \therefore \: \angle x = 126\degree}}} \red \dag

FINALLY,

  • The unknown  \bf \therefore \: \angle x = 126\degree

ADDITIONAL THEOREM :

  • Adjacent angles are equal to 180°

  • Corresponding angles are always equal.

  • Opposite vertical angles are always equal.

NOTE :

READ IT CAREFULLY.

Answered by anuekka508149
5

Given:

AB\bf \parallel∥ CD and CD\bf \parallel∥ EF

The ratio of \bf \angle∠ y and \bf \angle∠ z is 3:7.

\sf \underline {\orange {To \: find : }}

Tofind:

The unknown \bf \angle∠ x = ?

\sf \underline {\orange {\: Solution : }}

Solution:

We know that,

Corresponding angles are equal

HERE,

\bf \angle∠ y and \bf \angle∠ z are equal to 180° (linear pair).

So,

Let's assume that \bf \angle∠ y and \bf \angle∠ z is 3x and 7x.

According to the question,

\begin{gathered}\orange \leadsto \bf \: \: 3x \: + \: 7x = 180 \degree \: \\ \bf \implies \: 10x \: = 180 \: \degree \\ \bf \implies \:x \: = \frac{18 \cancel0}{1 \cancel0} \\ \bf \red \dag {\underline{ \boxed{ \bf x \: = \: 18 \: \degree}}{\red \dag }}\end{gathered}

⇝3x+7x=180°

⟹10x=180°

⟹x=

1

0

18

0

x=18°

HENCE,

\bf \angle∠ y = 3x = 3 × 18 =54°

\bf \angle∠ z = 7x = 7 × 18 = 126°

NOW,

We also know that

Adjacent angles are equal to 180°

THEREAFTER,

we can write it that :

\bf \angle∠ x and \bf \angle∠ y = 180° ( Adjacent angles are equal to 180°).

Substituting the value of \bf \angle∠ y :

\begin{gathered}\red \leadsto \bf\angle x \: + \: \angle \: y = 180° \\ \red \leadsto \bf \angle x \: + 54 \degree = 180\degree \\ \bf \red \leadsto \: \angle x = (180 - 54)\degree \\ \bf \red \dag{ \underline{ \boxed{\bf \therefore \: \angle x = 126\degree}}} \red \dag\end{gathered}

⇝∠x+∠y=180°

⇝∠x+54°=180°

⇝∠x=(180−54)°

∴∠x=126°

FINALLY,

The unknown \bf \therefore \: \angle x = 126\degree∴∠x=126°

ADDITIONAL THEOREM :

Adjacent angles are equal to 180°

Corresponding angles are always equal.

Opposite vertical angles are always equal.

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