Question

the adjacent angle of a parallelogram are (2 X + 12) and ( 3 x - 62 ) find the angles of parallelogram​

Answer 1

$\large\underline{ \underline{ \sf \maltese{ \: Question:- }}}$

• The adjacent angle of a parallelogram are (2x + 12) and ( 3 x - 62 ). find the angles of pparallelogram

$\large\underline{ \underline{ \sf \maltese{ \: Given:- }}}$

• First Adjacent Angle = $\blue{\fbox\orange{( \: 2x \: + \: 12 \: )}}$
• Second Adjacent Angle = $\blue{\fbox\orange{( \: 3x \: - \: 62 \: )}}$

$\large\underline{ \underline{ \sf \maltese{ \: Solution:- }}}$

Adjacent Angles of a Parallelogram are Supplementary.

$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\red{\: ( \: 2x \: + 12 \: ) \: + \: ( \: 3x \: - \: 62 \: ) \: = \: 180 }} }\\ \\\end{gathered}\end{gathered}\end{gathered}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ ( \: 2x \: + 12 \: ) \: + \: ( \: 3x \: - \: 62 \: ) \: = \: 180}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \: 2x \: + \: 3x \: + \: 12 \: - \: 62 \: = \: 180}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \:5x\: - \: 50 \: = \: 180}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \:5x\: = \: 180 \: + \: 50}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \:5x\: = \: 230}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ \:x\: = \: \cancel\frac{230}{5} }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{x \: = \: 46 }}}$

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Thus, The Adjacent Angles are :-

• (2x + 12) = 2 × 46 + 12 = $\green{\fbox\pink{104°}}$
• (3x - 62) = 3 × 46 - 62 = $\green{\fbox\pink{76°}}$

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Since, Opposite angles are equal :-

$\bf \therefore \; 1st \;angle = 104°$

$\bf \therefore \; 2nd \;angle = 76°$

$\bf \therefore \; 3st \;angle = 104°$

$\bf \therefore \; 4nd \;angle = 76°$

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More for Knowledge :-

• The opposite side of a parallelogram are parallel and equal.
• In a parallelogram, opposite angles are also equal.
• The diagonals of a parallelogram bisect each other
• Adjacent Angles in a Parallelogram are Supplementary.

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Answer 2

Step-by-step explanation:

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More for Knowledge :-

The opposite side of a parallelogram are parallel and equal.

In a parallelogram, opposite angles are also equal.

The diagonals of a parallelogram bisect each other

Adjacent Angles in a Parallelogram are Supplementary.

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