Question

The opposite angles of a parallelogram are (3x + 5)°and (61 − x)°.
Find the measure of four angles.

Answer 1

Given :

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

To Find :

Measure of four angles of parallelogram

Solution :

We know that ,

$\orange{\bigstar}$ " Opposite angles of a parallelogram are equal "

$\green{\bigstar}$ " Adjacent angles of a parallelogram are supplementary "

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

⇒ ( 3x + 5 ) = ( 61 - x )

⇒ 3x + 5 = 61 - x

⇒ 3x + x = 61 - 5

⇒ 4x = 56

⇒ x = 14°  $\purple{\bigstar}$

Let adjacent angle of x be y ,

Adjacent angles of a parallelogram are supplementary

⇒ x + y = 180

⇒ 14 + y = 180

⇒ y = 180 - 14

⇒ y = 166°  $\red{\bigstar}$

So ,

Four angles are 166° , 166° , 14° , 14°

Answer 2

Step-by-step explanation:

Sum of opposite angle of a parallelogram = 180°

So, According to Question,

3x + 5 + 61 - x = 180°

=> 2x = 180° - 66° = 114

=> x = 57°

then two opposite sides angles are (3x+5) = 171+5 = 176° and (61-x) = 61 - 57 = 4°

And we know consecutive angle are also supplement of each other.

So other angles = (180-176)° = 4°

and (180-4)° = 176°

Hence all angles of || gm is 176° ,4° , 176° , 4°.

Here you go buddy. Best of Luck