Question

the sum of two opposite angles of a parallelogram is 130. find the measure of each of its angles

Answer 1

■Opposite angles of parallelogram are equal

■Let angle be 'x'

■Then , 2x = 130°
==》 x = 65°
■ Adjacent angles sum = 180°
==》 65° + x = 180°
==》 x = 180 - 65 = 115°
■ALL ANGLES ARE = 65°, 115°, 65°, 115° .

Answer 2

Let ABCD be a parallalogram

Side AB = CD [opposit sides of a parallalogram are equall and parallel]

Side AD = BC [........................do...........................................................]

Side  [AB+CD] =130 given

⇒∡ A = ∡ C   [opposit angles of a parallalogram are equall ]

⇒∡ A + ∡ C =130 [given]

⇒∡ A = ∡ C =130/2=65

LET ∡B and ∡D  =X   [opposit angles of a parallalogram are equall ]

⇒∡A+∡B+∡C+∡D=360  [Sum of angles of parallalogram =360 ]

⇒∡65+2X+∡65=360

⇒2X+130=360

⇒2X=360-130

⇒2X=230

⇒X=230/2

⇒X=115

∴∡ A=65      Ans

∴∡B=115       Ans

∴∡C=65       Ans

∴∡D=115       Ans