Two angles form a linear pair.

Question

Two angels form a linear pair. The measure of one angle it 45 degrees more than the measure of the other angle. Write and solve an algebraic equation to find the measure of each angle 

Answer 1

In words

 

if the two angles form a linear pair, then the sum of the two angles equals 180 degrees.

 

We now have an equation in two unknowns

 

(i) angle one plus angle two equals 180 degrees

 

We can also state the number of degrees of one angle with respect to the other angle

 

(ii) angle two equals angle one plus 45 degrees

 

plugging (ii) into one gives us an equation with one unknown which is solveable

 

(iii) angle one plus angle one plus 45 degrees equals 180 degrees

 

In an algebraic equation we use variables which we define to be the unknown qualities

for example we could let X = degrees in angle one,  and Y = degrees in angle two

 

Now solve for X in (i) and (ii) above by using (iii) with the words replaced with  algebraic symbols

Then plug this value of X into (ii) to find Y

 

Final step is to check your values of X and Y by plugging them into (i) and seeing if it is true

 

Answer 2

Let x = the measure of the smaller angle

Let x + 45 = the measure of the larger angle

x + x + 45 = 180

2x = 135

x = 67.5°

x + 45 = 112.5°