Question

1. given that ∠klm is a straight angle, find m∠kln and m∠nlm.

(10x - 5)° (4x + 3)°
k l m
m∠kln =
°, m∠nlm =
°

Explanation:

Step1: Set up equation based on straight - angle

Since $\angle KLM$ is a straight angle and its measure is $180^{\circ}$, we have $(10x - 5)+(4x + 3)=180$.

Step2: Combine like - terms

Combining the $x$ terms and the constant terms, we get $10x+4x-5 + 3=180$, which simplifies to $14x-2 = 180$.

Step3: Solve for $x$

Add 2 to both sides of the equation: $14x=180 + 2=182$. Then divide both sides by 14: $x=\frac{182}{14}=13$.

Step4: Find $m\angle KLN$

Substitute $x = 13$ into the expression for $\angle KLN$: $m\angle KLN=10x-5=10\times13-5=130 - 5=125^{\circ}$.

Step5: Find $m\angle NLM$

Substitute $x = 13$ into the expression for $\angle NLM$: $m\angle NLM=4x + 3=4\times13+3=52+3=55^{\circ}$.

Answer:

$m\angle KLN = 125^{\circ}$, $m\angle NLM = 55^{\circ}$