Question

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

Answer 1

Answer:

Answer

Let four angles of given parallelogram taken in order be ∠A,∠B,∠Cand∠D respectively

Here opposite angles given ∠A=(3x−2)and∠C=(x+48)

We know that opposite angles of a parallelogram are equal

∴3x−2=x+48

2x=50

x=25

∴3x−2=73°

∠A=∠C=73°

Also we know that sum of two adjacent angles of a parallelogram is 180

∴∠A+∠B=180°

73°+∠B=180°

∠B=107°=∠D (Opposite angles are equal)

∴ All four angles of given parallelogram are 73°,107°,73°,107°

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.