Question

Angles LMN and NOP are complementary angles. m < LMN = 3x and m < NOP = ( 4x + 1 ). What is the simplified equation that will solve for x? A: 7x + 1 = 90 B: 8x = 90 C : x + 1 = 90 D: 7x - 1 = 90

Answer 1

Complementary angles sum to 90 degrees. Therefore, we can set up the equation based on the given measures of angles LMN and NOP.

Given:
- \( m\angle LMN = 3x \)
- \( m\angle NOP = 4x + 1 \)

Since they are complementary, we have:
\[
m\angle LMN + m\angle NOP = 90
\]
Substituting the expressions for the angles:
\[
3x + (4x + 1) = 90
\]
Now, simplify the equation:
\[
3x + 4x + 1 = 90
\]
\[
7x + 1 = 90
\]

Thus, the simplified equation that will solve for \( x \) is:
\[
\boxed{7x + 1 = 90}
\]

Therefore, the answer is A: \( 7x + 1 = 90 \).