Question

4. The adjacent angles of a parallelogram are (2x - 4)º and (3x – 1)º.
Find the measures of all angles of the parallelogram.​

Answer 1

Answer:

two equal angles of 70° and two equal angles of 110°.

Step-by-step explanation:

let one angle be = ( 2x-4 )°

let it's adjacent angle be = ( 3x-1 )°

therefore, the other two angles are = (2x-4)° and (3x-1)° [ as the opposite angles of a parallelogram are equal, and the r four angles in it , so the rest two angles will be the same as they both should have pairs.]

Now, we know , sum of all the angles of a quadrilateral ( in this case it's the parallelogram ) is = 360°

so the equation would be like :-

=> 2(2x-4) + 2(3x-1) = 360

=> 4x-8 + 6x-2 = 360

=> 10x-10 = 360

=> 10x = 370

=> x = 37°

therefore, the two adjacent angles are :-

Angle one => 2×37 - 4 = 70°

Angle adjacent to it => 3×37 - 1 = 110°

hence , there opposite angles will also be equal to them.

Hope it helped !

thanks !!