Question

please anyone explain with steps the answer is 101°,79°​

Answer 1

$\huge{ \mathbf{ \underline{ \underline{{ \color{goldenrod}{❁} \pink{Question:- }}}}}}$

If the two opposite angles formed at the point of

ntersection of the diagonals of a parallelogram

are 2x+61° and 3x+ 41°, find the adjacent angle

formed at the point.

✿Given:-

• the two opposite angles formed at the point of intersection of the diagonals of a parallelogram are 2x+61° and 3x+ 41°.

❀To find:-

• Adjacent angles formed at the point.

᯽︎Solution:-

• $\large{ \boxed{ \sf{ \underline{ \pink{Opposite \: angles \: of \: parallelogram \: are \: equal}}}}}$

• $\purple{ \dag} \: \: \: \: \: \: \sf{So \: \angle \:AOD= \angle{COB}}$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \red{ \implies} \bf \: 2x + 61 \degree = 3x + 41 \degree$

$\\ \: \: \: \: \: \: \: \: \: \: \pink{ : \implies} \bf \: 3x - 2x = 61 - 41 \degree$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \purple{: \implies} \bf \: x = 20 \degree$

• Now by keeping the value of x we will find the measure of ∠AOD and ∠COB

$\\ \: \: \: \: \: \: \: \: \: \: \: \orange{: ↦ } \angle \: \bf \: AOD = 2 \times 20 + 61 \degree \\ \: \: \: \: \: \color{aqua}{: ↦} \: 40 \degree + 61 \degree \\ \: \: \: \: \: \: \: \color{goldenrod}{ : ↦ } \: \: \: \: \: 101 \degree$

$\\ \: \: \: \: \: \: \: \red{ : ↦} \angle \bf \:COB \: = 3 \times 20 \degree + 41 ^{o} \\ \: \: \: \: \: \: \color{maroon} : ↦ \bf \: 60 ^{o} + 41 ^{o} \\ \: \: \: \: \: \: \: \: \color{aqua} : ↦ \: 101 ^{o}$

Adjacent angles are ∠AOD and ∠COB:-

↠∠BOC + ∠DOC=180°

↠3x+ 41° + ∠DOC=180°

↠101 +∠DOC=180°

↠∠DOC=180°-101

↠∠DOC=79°

$\sf \: ↠∠DOC=∠AOB \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: (opposite \: angles \: of \: a \: || grm \: are \: equal)$

Similarly ∠AOB=79°

• Hence the answers ∠AOB=101° and ∠COD=79°

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Answer 2

Answer:

sorry

Step-by-step explanation:

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