Question

The adjacent angles of a parallelogram measure (4x – 10)˚ and ( x+15)˚ .Find the value of x.​

Answer 1

Answer:

Solution:

Let ABCD is a parallelogram.

<A = 3x+10, <B = x+20

<A+<B = 180°

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Sum of Adjecent angles

are supplementary in a parallelogram.

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3x+10+x+20 = 180°

=> 4x = 180-30

=> 4x = 150

=> x = 150/4

=> x = 37.5°

Now ,

<A = <C = 3x+10

= 3×37.5+10

= 122.5°

And

<B = <D = x+20

= 37.5 + 20

= 57.5°

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Opposite angles are equal

in a parallelogram

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Answer 2

The value of x is 35.

Step-by-step explanation:

${\underline{\underline{\bf{Given:}}}}$

• That, the adjacent angles of a parallelogram measures (4x – 10)° and (x + 15)°

${\underline{\underline{\bf{Need\:to\: find:}}}}$

• The value of 'x'.

${\underline{\underline{\bf{Concept:}}}}$

• The adjacent angles of a parallelogram are supplementary, i.e, the sum of the two consecutive angles will be 180°.

${\underline{\underline{\bf{Solution:}}}}$

As we know, the sum of the two angles is 180°, we can form an equation:

$\leadsto{\boxed{\sf{\purple{\angle A+\angle B=180°}}}}$

Now, by inserting the measures and solving the equation,

$\:\:\:\:\:\:\::\implies{\sf{(4x-10)+(x+15)=180}}$

$\:$

$\:$

Grouping the like terms-

$\:\:\:\:\:\:\:\:\:\:\:\::\implies{\sf{4x+x-10+15=180}}$

$\:$

$\:$

Adding/subtracting the like terms-

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\sf{5x+5=180}}$

$\:$

$\:$

Transposing LHS (5) to RHS (Subtraction)-

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\sf{5x=180-5}}$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\sf{5x=175}}$

$\:$

$\:$

Again transposing LHS (5) to RHS (Division)-

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\sf{x=\dfrac{\cancel{175}}{\cancel{5}}}}$

$\:$

$\:$

Cancelling 175 as it is a multiple of 5-

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\::\implies{\boxed{\frak{\red{35}=x}}}$

${\underline{\underline{\bf{Verification:}}}}$

To verify, substitute 35 in places of x in the equation.

$\implies{\sf{\angle A+\angle B=180\degree}}$

$\implies{\sf{(4x-10)\degree+(x+15)\degree=180\degree}}$

$\implies{\sf{(4\times 35-10)\degree+(35+15)\degree=180\degree}}$

$\implies{\sf{(140-10)\degree+50\degree=180\degree}}$

$\implies{\sf{130\degree+50\degree=180\degree}}$

$\implies{\sf{180\degree=180\degree}}$

$\implies{\sf{L.H.S.=R.H.S}}$

• Therefore, the value of x is 35.

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