Question

Given that lines m and n are parallel, find the measure of angle1​

Answer 1

Given

Line m and n are parallel

Let line l be the transverse.

Refer to attachment

Let Angle A = x + 30

Angle B = x^2

Angle C = Angle 1 = ??

Now since l is transverse

=> Angle A = Angle B

(Because alternate exterior angles are equal for parallel lines)

Therefore,

$x^{2} = x+30$

$x^{2} - x - 30 = 0$

Solving the quadratic equation

$x^{2} - 6x + 5x -30 = 0$

x(x-6) +5(x-6) = 0

(x-6)(x+5) = 0

Either

x-6 = 0   or x+5=0

Either

x=6 or x= -5

Thus Angle A = Angle B = 25 (for x= -5) or 36 (for x=6)

As m is straight line

Angle B + Angle C = 180  (Linear pair)

Angle C = 180 - Angle B

Angle 1 = 180 - Angle B

• For Angle B = 25, Angle 1 = 180 - 25 = 155
• For Angle B = 36, Angle 1 = 180 - 36 = 144

Thus Angle 1 will measue 155 or 144