Question

If the measure of angle 1 is 55 degree then find the measure of angle 4

Answer 1

Answer: 220°

Step-by-step explanation:

As ∠1 = 55°

∴   ∠4 = 220°

Answer 2

As per the intersecting lines theorem we can find the angle 4 as 125 degrees.

Calculation

When 2 lines intersect we can say that the vertically opposite angles are equal in measure.

We can say that

$m < 1= m < 3=55\\\\m < 2=m < 4$

Overall,

$m < 1+m < 2+m < 3+m < 4 = 360 \\55+m < 2+ 55+ m < 4= 360\\110 +m < 2+m < 4= 360 \\m < 2+m < 4= 360- 110 = 250$

Measure of angle 4 can be found as,

$m < 4 = m < 2= \frac{250}{2} \\m < 4=m < 2= 125$

So m<4 was found as 125 degrees.

So option (a) is the correct answer.

Here the complete question is

If the measure of angle 1 is 55 degree then find the measure of angle 4