Question

1. point m is in the interior of ∠lkn. if m∠lkm = 5x - 10 and m∠mkn = 3x + 20, and ∠lkn is a right angle, find the measure of ∠lkm. a) 10 b) 40 c) 50 d) 90

Explanation:

Step1: Use angle - addition postulate

Since point $M$ is in the interior of $\angle LKN$ and $\angle LKN$ is a right - angle ($m\angle LKN = 90^{\circ}$), we have $m\angle LKM+m\angle MKN=m\angle LKN$. Substituting the given expressions, we get $(5x - 10)+(3x + 20)=90$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $5x+3x-10 + 20=90$, which simplifies to $8x+10 = 90$.

Step3: Solve for $x$

Subtract 10 from both sides: $8x=90 - 10=80$. Then divide both sides by 8: $x=\frac{80}{8}=10$.

Step4: Find the measure of $\angle LKM$

Substitute $x = 10$ into the expression for $m\angle LKM$. So $m\angle LKM=5x-10=5\times10-10=50 - 10 = 40$.

Answer:

B. 40