Angles LMN and NOP are complementary angles. m ∠ LMN=3x° and m ∠ NOP=(4x +1)°

Question

What is the simplified equation that will solve for x?

(1 point)
Responses

x+1=90x plus 1 is equal to 90

7x+1=907 x plus 1 is equal to 90

7x−1=907 x minus 1 is equal to 90

8x = 90

Answer 1

Since angles LMN and NOP are complementary angles, their measures add up to 90 degrees. Therefore, we can write the equation:

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

Substituting the expressions for the angles, we have:

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

Now, combine like terms:

\[ 3x + 4x + 1 = 90 \] \[ 7x + 1 = 90 \]

This is the simplified equation that will solve for \( x \).

So, the correct response is:

7x + 1 = 90.