Question

If opposite angles of rhombus are (3x-18) and (5x-80) then find measures of angles

Answer 1

Answer:

45° , 135° , 45° , 135°

Step-by-step explanation:

Given----> Opposite angles of rhombus are

( 3x - 18 ) and ( 5x - 80 ) .

To find-----> Find measure of angles.

Solution----> Plzz see the attachement , now,

Let in rhombus ABCD,∠A = (3x - 18 ) and ∠ C = ( 5x - 80 )

We know that , opposite angles of rhombus are equal ,so ,

∠ A = ∠ C

=> ( 3x - 18 ) = ( 5x - 80 )

=> 80 - 18 = 5x - 3x

=> 62 = 2 x

=> x = 62 / 2

=> x = 31

∠ A = 3x - 18

= 3 ( 31 ) - 18

= 63 - 18

=> ∠A = 45

∠ A = ∠ C = 45°

We know , that sum of adjacent angles of rhombus is 180° , so ,

∠ A + ∠ D = 180°

=> 45° + ∠D = 180°

=> ∠D = 180° - 45°

=> ∠ D = 135°

But, ∠ D = ∠ B = 135° ( opposite ∠' s of rhombus )

Answer 2

Answer:

75 degrees

Step-by-step explanation: