Qstnid -A-1- In Parallelogram Abcd, ∠A = 3 Times ∠B. Find All The Angles Of The Parallelogram. In The Same Parallelogram, If Ab = 5x - 7 And Cd = 3x + 1 ; Find The Length Of Cd. - 17: Special Types Of Quadrilaterals Class 8 Maths - Icse-viii-mathematics

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ICSE-VIII-Mathematics

17: Special Types of Quadrilaterals Class 8 Maths

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#1
In parallelogram ABCD, ∠A = 3 times ∠B. Find all the angles of the parallelogram. In the same parallelogram, if AB = 5x - 7 and CD = 3x + 1 ; find the length of CD.
Ans :
Let ∠B = x
∠A = 3 ∠B = 3x
AD || BC
∠A + ∠B = 180°
3x + x = 180°
⇒ 4x = 180°
⇒ x = 45°
∠B = 45°
∠A = 3x = 3 x 45 = 135°
and ∠B = ∠D = 45°
opposite angles of ||gm are equal.
∠A = ∠C = 135°
opposite sides of //gm are equal.
AB = CD
5x - 7 = 3x + 1
⇒ 5x - 3x = 1+7
⇒ 2x = 8
⇒ x = 4°
CD = 3 x 4 + 1 = 13
Hence, 135°, 45°, 135° and 45°; 13