Question

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

Answer 1

[Refer to the image]

Given opposite angles of a parallelogram are (2x+10)° and (3x-15)°

We know that opposite angles of a parallelogram are equal

$2x + 10 = 3x - 15$

$3x - 2x = 10 + 15$

$x = 25$

Substituting value of x in the given angles

$2x + 10 = 2(25) + 10$

$D= 50 + 10 = 60 \: degrees$

$3x - 15 = 3(25) - 15$

$B = 75 - 15 = 60 \: degrees$

Finding the adjacent angles

In a parallelogram the sum of adjacent angles is 180°

Angle D + Angle C = 180°

$60 + y = 180$

$y = 120 \: degrees$

y = Angle C and Angle C = Angle A [because they're opposite angles]

Measure of each angle = 120°, 60°, 120°, 60°

Hope this helps! ^^

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.