In a parallelogram ABCD, angle C=(3x-5) and angle D=(2x+15) then value of x is (a)32 (b)30 (c)42 (d)34
Answers
Answer:
Step-by-step explanation:
angle c and d are adjacent angles so their sum will be 180
3x-5 + 2x+15 = 180
5x + 10 = 180
5x=170
x=34
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Given : In a parallelogram ∠A =(2x + 35), ∠C= (3x - 5)
To find : Value of x, m∠A , m∠B , m∠C, m∠D=?
Solution:
Quadrilateral ABCD is A parallelogram.
∴∠A=∠C .........Opposite angles of parallelogram
∴ 2x + 35 = 3x - 5
∴ 35 + 5 = 3x - 2x
∴ 40 = x
∴ x = 40
∴∠A = ∠C = 2x + 35
= 2 x 40 +35
= 80 + 35
∴ ∠A= ∠C = 115°
Adjacent angles of parallelogram are Supplementary
∴ ∠A + ∠B = 180°
∴ 115 + ∠B = 180
∴ ∠B = 180 - 115
∴ ∠B = 65°
∠B = ∠D = 65°.......Opposite angles of parallelogram.
∴ X = 40
∴m∠A = m∠C = 115°
∴m∠B = m∠D = 65°
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