Question

In the figure BL, AM and CN are parallel to each other and AP, BQ are also parallel to each other, then
x°-y°+ 22° is​

Answer 1

NDP and ADC are vertically opposite angles. If, NDP = 3z, then ADC is also = 3z.

ADC and DCB are co- interior angles. So, their sum is = 180 degrees.

ADC+DCB = 180 degrees

3z+105 degrees = 180 degrees

3z = (180-105) degrees

z = 75/3 degrees

z = 25 degrees.

AM and CN are parallel to each other. So, MAP = NDP

3z = 2y

3*25(value of z = 25) = 2y

75/2 = y

y = 37.5 degrees.

LDC and NCB are co- interior angles. So, their sum is = 180 degrees

x+105 = 180 degrees

x = 75 degrees.

Now, x degree+y degree+22 degree = 75+37.5+22 = 134.5 degrees