Question

Angles LMN and NOP are complementary angles. m < LMN = 3x and m < NOP = ( 4x + 1 ). What is the simplified equation that will solve x ?

Answer 1

Since angles LMN and NOP are complementary, their measures add up to 90 degrees. We can set up the equation as follows:

\[
m \angle LMN + m \angle NOP = 90
\]

Substituting in the given expressions for the angles:

\[
3x + (4x + 1) = 90
\]

Now we can simplify this equation:

\[
3x + 4x + 1 = 90
\]

Combine like terms:

\[
7x + 1 = 90
\]

To isolate \(7x\), subtract 1 from both sides:

\[
7x = 90 - 1
\]

\[
7x = 89
\]

Thus, the simplified equation to solve for \(x\) is:

\[
7x = 89
\]