Question

the opposite angles of a parallelogram are (3x+5)° and (61-x)° , find the measure of pair of other opposite angles​

Answer 1

Answer :-

Accoding to the properties of parallelogram -

• The opposite angles of a parallelogram are equal.

• The sum of adjacent angles of a parallelogram is 180°.

According to the question :-

⇒ 3x + 5 = 61 - x

⇒ 3x + x = 61 - 5

⇒ 4x = 56

⇒ x = 56/4

⇒ x = 14

Angles of Parallelogram = 61 - x

= 61 - 14

= 47°

Two angles of Parallelogram = 47°

By using the property -

The sum of adjacent angles of a parallelogram is 180°.

Let the adjacent angle be y

⇒ 47 + y = 180

⇒ y = 180 - 47

⇒ y = 133°

So the angles of parallelogram are - 47° , 133° , 47° and 133°.

Answer 2

ɢɪᴠᴇɴ :-

• The opposite angles of a parallelogram are (3x + 5)° and (61 − x)°

ᴛᴏ ꜰɪɴᴅ :-

• The measure of pair of other opposite angles.

ꜱᴏʟᴜᴛɪᴏɴ:-

We know that

$\green{\sf \red{\mapsto}\:Opposite\; angles\; of\; a\: parallelogram\; are\; equal\:}$

$\purple{\sf \orange{\mapsto}\:Adjacent\; angles\; of\; a\: parallelogram \;are\; supplementary\; }$

According to the given condition,

$:\implies\tt 3x + 5 = 61 - x$

$:\implies\tt 3x + x = 61 - 5$

$:\implies\tt 4x = 56$

$:\implies\tt x = \dfrac{56}{4}$

$:\implies\tt x = 14$

Now,

The Angles of Parallelogram = 61 - x

$:\implies\tt 61 - 14$

$:\implies\tt 47°$

Two angles of Parallelogram = 47°

We know,

The sum of adjacent angles of a parallelogram is 180°.

Let the adjacent angle be "z"

So,

$:\implies\tt 47 + z = 180$

$:\implies\tt z = 180 - 47$

$:\implies\tt z = 133°$

Therefore, the angles of parallelogram are - 47° , 133° , 47° and 133°.

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