Two adjacent angles of a parallelogram are (3x+20 and (2x+10 then the value of x is))

Given: ∠A = (3x + 12)˚ and ∠B = (2x - 32)˚ Opposite angles of a parallelogram are equal. ∴ ∠C = ∠A     ….(i) ⇒ ∠C = (3x + 12)˚ ∠D = ∠B        ….(ii) ∠D = (2x - 32)˚ In a quadrilateral, the sum of all the angles is equal to 360˚. ∴ In ABCD, ∠A + ∠B + ∠C  + ∠D = 360˚ ∴ 3x + 12 + 2x - 32 + 3x + 12 + 2x - 32 = 360 10x - 40 = 360 10x = 360 + 40 = 400

⇒ x = `400/10` = 40

∴ ∠A = (3x + 12)˚ ∴ ∠A = 3 × 40 +12∴ ∠A = 120 + 12 ⇒ ∠A = 132˚ ∴ ∠C = 132˚        .......[From (i)] ∠B = (2x - 32)˚ ∴ ∠B = 2 × 40 - 32 ∴ ∠B = 80 - 32 ⇒ ∠B = 48˚ ∴ ∠D = 48˚        ........[From (ii)] Hence measure of x is 40.

Also, measures of ∠C and ∠D are 132˚ and 48˚ respectively.

Uh-Oh! That’s all you get for now.

We would love to personalise your learning journey. Sign Up to explore more.

Sign Up or Login

Skip for now

Uh-Oh! That’s all you get for now.

We would love to personalise your learning journey. Sign Up to explore more.

Sign Up or Login

Skip for now

Join NOW to get access to exclusive study material for best results