Question

<1 and <2 form a linear pair. If m<1= 4m<2, find the measure of each of the two angles.

Answer 1

Answer:

• The angle ∠1 = x = 36°

• The angle ∠2 = 4x = 4(36°) = 144°

Step-by-step explanation:

We know that when two lines meet or intersect, we get a linear pair of angles.

Linear pairs are basically two adjacent angles that form a line.

The measure of two adjacent angles forming a straight line is 180, meaning they are supplementary.

We are given that <1 and <2 forms a linear pair, and

m∠1 = 4m∠2

It means the angle ∠1 is 4 times the measure of angle ∠2.

Let the angle ∠1 be = x

As the angle 1 is 4 times the measure of angle ∠2, so

The angle 2 will be = 4x

As <1 and <2 forms a linear pair, thus the measure of the sum of <1 and <2 will be 180°, so

x + 4x = 180

5x = 180

divide both sides by 5

5x/5 = 180/5

x = 36°

Therefore,

• The angle ∠1 = x = 36°

• The angle ∠2 = 4x = 4(36°) = 144°