Question

∠LMN and ∠PQR are complementary angles. Find m∠LMN if m∠LMN=(4x−2) ∘ and m∠PQR=(9x+1) ∘

Answer 1

To find the measure of θLMN, which is complementary to θPQR, set up the equation (4x−2) + (9x+1) = 90 and solve for x. Then, substitute the value of x into mθLMN=(4x−2)° to get the final answer.

Step-by-step explanation:

θLMN and θPQR are complementary angles. To find mθLMN given mθLMN=(4x−2)° and mθPQR=(9x+1)°, we need to use the fact that the sum of complementary angles is 90°. Setting up the equation:

4x − 2 + 9x + 1 = 90

Simplifying the equation gives us:

13x − 1 = 90

Add 1 to both sides:

13x = 91

Divide both sides by 13:

x = 7

Now, we substitute x back into the expression for mθLMN:

mθLMN = 4(7) − 2

mθLMN = 28 − 2

mθLMN = 26°

The measure of angle LMN is 26°.