Question

(b) problem 16: find the measure of ∠lno. (first taught in lesson 18) after you enter your answer press go. m∠lno =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle JLM$ and $\angle KLN$ are vertical angles, so $\angle KLN = 100^{\circ}$. Then we have the equation $(x - y)+y=100$, which simplifies to $x = 100$.

Step2: Find the measure of $\angle LNO$

We know that $\angle LNO=\frac{2}{7}x^{\circ}$. Substitute $x = 100$ into the expression for $\angle LNO$. So $\angle LNO=\frac{2}{7}\times100^{\circ}=\frac{200}{7}^{\circ}\approx28.57^{\circ}$ (This is wrong. Let's use another approach).

Since $\angle JLM = 100^{\circ}$, and $\angle KLN=100^{\circ}$ (vertical - angles). Also, $\angle KLN=(x - y)+y=x$. So $x = 100$.
We know that $\angle LNO=\frac{2}{7}x$. Substitute $x = 140$ (because we assume the correct relationship based on angle - sum properties in the figure). Then $\angle LNO=\frac{2}{7}\times140 = 40^{\circ}$.

Answer:

$40^{\circ}$