SOLUTION: Two angles form a linear pair. The measure of one angle is 26∘ greater than the measure of the other angle. Find the measure of each angle.
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Question 1121788: Two angles form a linear pair. The measure of one angle is 26∘ greater than the measure of the other angle. Find the measure of each angle.
You can put this solution on YOUR website! the two angles which form a linear pair are supplementary, they always add to °
let's say one angle is and the other angle is
by definition, ° ........eq.1
if the measure of one angle is ° greater than the measure of the other angle, we have
°....eq.2
substitute from eq.2 in eq.1
° ........solve for °
°
°
°
go to eq.2 and calculate
x + y = 180 degrees, (where x is the larger angle measure)
x - y = 26 degrees.
Add the two equations. You will get
2x = 180 + 26 = 206 ====> x = 206/2 = 103 degrees.
Answer. One angle is 103 degrees. The other angle is 103 - 26 = 77 degrees.
Check. 103 + 77 = 180 degrees. ! Correct !
Solved.
Another way to solve it is THIS :
Let y be the degree measure of the smaller angle.
Then the larger angle degree measure is (y+26), and their sum is 180 degrees:
y + (y + 26) = 180
2y + 26 = 180
2y = 180 - 26 = 154
====> y = 154/2 = 77 degrees, and you get the same answer.
