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.

Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source): 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

°....eq.2
°
°




Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
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.

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