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Answer:
We conclude that
- The angle ∠1 = x = 36°
- The angle ∠2 = 4x = 4(36°) = 144°
Step-by-step explanation:
Given
<1 and <2 form a linear pair
m∠1 = 4m∠2
To determine
Find the measure of each of the two angles.
<u>Important Points about linear pair:</u>
- 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.
As
<1 and <2 form a linear pair
m∠1 = 4m∠2
In other words, 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
divide both sides by 5
Thus, we conclude that
- The angle ∠1 = x = 36°
- The angle ∠2 = 4x = 4(36°) = 144°