Question

Find the values of x and y in each case.
TERM is a parallelogram

Answer 1

Answer:

x = 20

Step-by-step explanation:

MTE + RET = 180⁰. (sum of two adjacent angles of a parallelogram is 180⁰)

3x-10 + 5x+30 = 180

8x + 20 = 180

8x = 160

x = 160/8

x = 20

HAPPY TO HELP!

Answer 2

Appropriate Question :

TERM is a parallelogram. Find the values of x in each case.

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Solution :

The value of x is 20°

• ∠T = 50°
• ∠E = 130°
• ∠R = 50°
• ∠M = 130°

PROOF :

In parallelogram,

Sum of all angles = 360°

$\bf⇝ \: ∠T + ∠E + ∠R + ∠M = 360 \degree$

$\bf⇝ \: 50\degree + 130\degree + 50\degree + 130\degree = 360\degree$

$\bf⇝ \: 360\degree = 360\degree$

Hence, proved !!

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Step-by-step Explanation :

Given that,

TERM is a parallelogram

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To find,

The value of x

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Let,

• ∠T = 3x-10
• ∠E = 5x+30

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We know that,

In parallelogram

The adjacent angles are supplementary

• (Supplementary = 180°)

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Here,

∠T and ∠E are adjacent angles

$⟹ \: \bf 3x-10 + 5x+30 = 180°$

$⟹ \: \bf 8x + 20 = 180°$

$⟹ \: \bf 8x = 180 \degree - 20 \degree$

$⟹ \: \bf 8x = 160\degree$

$\displaystyle⟹ \: \bf x = \frac{ \cancel{ 160 } \: ^{20} }{ \cancel{8} \: _{1} }$

$\displaystyle \red{⟹ \: \underline{\boxed{ \bf x = 20 \degree}}}$

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$\red \star \: \boxed{ \large \tt∠T = 3x-10}$

Where,

x = 20°

$\bf \implies 3x-10$

$\bf \implies3(20) - 10$

$\bf \implies60 - 10$

$\bf \implies50 \degree$

Hence,

∴ ∠T = 50°

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$\red \star \: \boxed{ \large \tt∠E = 5x+30}$

Where,

x = 20°

$\bf \implies5x+30$

$\bf \implies5(20)+30$

$\bf \implies100+30$

$\bf \implies130 \degree$

Hence,

∴ ∠E = 130°

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In parallelogram,

The opposite angles are equal

So,

• ∠R = 50°
• ∠M = 130°

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