Question

In a parallelogram ABCD, if angle A = (2x+15)°, angle B = (4x-27)° then find the value of x and the measure of angle C and angle D​

Answer 1

Answer:

: 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°

Answer 2

Answer:

Step-by-step explanation

we know adjacent angles of parallelogram are suplementry angles.

angle A+angle B=180

2x+15+4x-27=180

6x-78=180

6x=180-78

6x=102

x=102/6

x=17

2x+15=49(angle A)

4x-27=41(angle B)

sum of all angles of a parallelogram is 360°

Let C and D be x

A+B+C+D=360°

49+41+x+x=360°

2x+90=360°

2x=360-90

2x=270

x=270/2

x=135

49+41+135+135=360°

Hope this help