Question

the opposite angles of a parallelogram are 2x+10 degreeand 3x-15 degree find the each angle measurement of parallelogram​

Answer 1

Step-by-step explanation:

As, opposite angles of parallelogram are equal

1st angle = 2x+10, 2nd angle = 3x-15

3rd angle = 2x+10, 4th angle = 3x-15

As, sum of all angles in a parallelogram = 360°

(2x+10) + (3x-15) + (2x+10) + (3x-15) = 360

10x -10 = 360

10x = 360+10

10x = 370

x = 370/10

x = 37°

1st angle = 2 X 37 + 10 = 84°

2nd angle = 3 X 37 - 15 = 96°

3rd angle = 2 X 37 + 10 = 84°

4th angle = 3 X 37 - 15 = 96°

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Answer 2

$\large\underline{\pmb{\sf Property...}}$

• $\sf\green{Opposite\:Angles\:of\:parallelogram\:are\:equal}$

$\large\underline{\pmb{\sf Required\:Solution....}}$

• According, to the given identity, the given angles are equal.

$\therefore \sf 2x+10=3x-15$

$:\implies \sf10+15=3x-2x$

$:\implies\boxed{\sf x=25°}$

• As we got the required value of x, let's calculate the angles.
• For that, we just have to put the value of x in the given equation of angles.

$\underline{\rm{\sf 1st \:Angle :- }}$

$:\implies \sf 2x+10$

$:\implies\sf 2(25)+10$

$:\implies 50+10=\red{60°}$

$\underline{\rm{\sf 2nd\:Angle:-}}$

$:\implies \sf 3x-15$

$:\implies \sf 3(25)-15$

$:\implies\sf 75-15 = \red{60°}$

━━━━━━━━━━━━━━━━━━━━━━

Done :D

ADDITIONAL INFORMATION:-

• Opposite sides of a parallelogram are equal.
• adjacent angles of a parallelogram are supplementary i.e their sum is 180°
• Diagonals of a parallelogram bisect each other
• Each diagonal of a parallelogram separates it into two congruent triangles.