∠1 and ∠2 are a linear pair. ∡1=x−50 and ∡2=x+32 . Find the measure of each angle. (2 points)

Answer 1

So first piece of information provided in this question is that angles 1 and 2 are a linear pair. This means that the sum of angles 1 and 2 is 180^o.

The next step in solving this problem is writing out our equation:

∡1+ ∡2 = 180

next substitute the values given:

(x−50) + (x+32) = 180

then solve the equation for x

2x−18 =180

2x = 198

x=99

Then substitute the x value for each angle:

∡1=x−50 --> ∡1= 99-50 = 49^o

∡2=x+32 --> ∡2 = 99+32 = 131^o

Then to check calculations you can add the values for both angles to confirm they add up to 180^o

49^o + 131^o = 180^o

Answer 2

NOTE: WHEN THIS PROBLEM WAS FIRST POSTED m<2=x+29. IT WAS SUBSEQUENTLY CHANGED TO m<2=x+32. BOTH SOLUTIONS ARE PROVIDED BELOW.

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Angle 1 and angle two from a linear pair. This means:

1. These two angles share a common vertex;

2. These two angles share one common side; and

3. The the two sides of these angles that are not the common side form a straight line.

One consequence of this is that the sum of the measures of these two angles is 180 degrees.

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CURRENT SOLUTION:

Substituting the values given,

m<1 + m<2 = 180

(x-50) + (x+32) = 180

2x -50 + 32 = 2x -18 = 180

Adding 18 to both sides (to get the variable on one side of the equation, and the constant on the other side of the equation):

2x = 198

Dividing both sides by 2 (because we don't care what 2x is, we want to know what x is):

2x/2 = 1x = x = 198/2 = 99

We now know what x equals. But the problem asks for the value of each angle, NOT what x is.

m<1 = x - 50 = 99 - 50 = 49 degrees

m<2 = x + 32 = 99 + 32 = 131 degrees

Are we done? NO! We still need to verify that we have found the correct answer to the problem.

To do so, we need to confirm that the sum of the measures of these two angles equals 180 degrees.

49 + 131 = 180

And that verifies we have found the correct answer.

So m<1 = 49 degrees and m<2 = 131 degrees.

DON'T FORGET THE UNITS! Some teachers will count the whole problem wrong if you do.

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PREVIOUS PROBLEM SOLUTION:

Angle 1 and angle two from a linear pair. This means:

1. These two angles share a common vertex;

2. These two angles share one common side; and

3. The the two sides of these angles that are not the common side form a straight line.

One consequence of this is that the sum of the measures of these two angles is 180 degrees.

Substituting the values given,

m<1 + m<2 = 180

(x-50) + (x+29) = 180

2x -50 + 29 = 2x -21 = 180

Adding 21 to both sides (to get the variable on one side of the equation, and the constant on the other side of the equation):

2x = 201

Dividing both sides by 2 (because we don't care what 2x is, we want to know what x is):

2x/2 = 1x = x = 201/2 = 100.5

We now know what x equals. But the problem asks for the value of each angle.

m<1 = x - 50 = 100.5 - 50 = 50.5 degrees

m<2 = x + 29 = 100.5 + 29 = 129.5 degrees

Are we done? NO! We still need to verify that we have found the correct answer to the problem.

To do so, we need to confirm that the sum of the measures of these two angles equals 180 degrees.

50.5 + 129.5 = 180

And that verifies we have found the correct answer.

So m<1 = 50.5 degrees and m<2 = 129.5 degrees.

DON'T FORGET THE UNITS! Some teachers will count the whole problem wrong if you do.