the measure of angle 2 is 12 less than 5 times the measure of angle 1. If angle 1 and angle 2 form a linear pair find m angle 2

Answer 1

Let x = degree measure of angle 1.

Then 5x - 12 = degree measure of angle 2.

x + (5x - 12) = 180

Solve for x.

Answer 2

The important thing to note here is the definition of linear pairs. This means that angle 1 and angle 2 are adjacent supplementary angles. In other words, their measures add up to 180º. We can use this definition along with the rest of the information in the problem to write 2 equations, giving us a system of equations.

If angle 2 is m, let's call angle 1 n.

We know from the definition of a linear pair that:

m + n = 180.

Now from the rest of the problem, we just need to translate the words into an algebraic equation. If the measure of angle 2 (m) is 12 less than 5 times the measure of angle 1 (n), that means that we need to multiply angle 1 (n) by 5, and subtract 12 to get angle 2 (m). This can be written as the following equation.

m = 5n - 12

Now we have 2 equations:

(i) m + n = 180

(ii) m = 5n - 12

We can substitute 5n - 12 from equation ii for the value of m in equation i. We are then left with 1 equation with 1 variable:

5n - 12 + n = 180

Now solve for n:

5n - 12 + n = 180 -> combine like terms with n

6n - 12 = 180 -> add 12 to both sides

6n = 192 -> divide both sides by 6

n = 32

Now we know that the measure of angle n is 32, BUT the question asked for the measure of angle m. To do this, we have to plug in the value of 32 for n back into our original equation ii.

m = 5n - 12

m = 5(32) - 12

m = 148

We can also double check to make sure that our two values, 32 & 148 satisfy the condition of linear pairs:

32 + 148 = 180.

Measure of angle m is 148º