Question

find the indicated angle measure. 1. find m∠lmn 3. m∠abc = 95°. find m∠abd and m∠dbc

Explanation:

Step1: Solve for $m\angle LMN$

Since $\angle LMP = 85^{\circ}$ and $\angle PMN=23^{\circ}$, then $m\angle LMN=m\angle LMP + m\angle PMN$. So $m\angle LMN=85^{\circ}+ 23^{\circ}=108^{\circ}$.

Step2: Solve for $x$ in the second - part

We know that $m\angle ABC=m\angle ABD + m\angle DBC$. Given $m\angle ABC = 95^{\circ}$, $m\angle ABD=(2x + 23)^{\circ}$ and $m\angle DBC=(9x - 5)^{\circ}$. Then $(2x + 23)+(9x - 5)=95$. Combine like - terms: $2x+9x+23 - 5 = 95$, $11x+18 = 95$. Subtract 18 from both sides: $11x=95 - 18=77$. Divide both sides by 11: $x = 7$.

Step3: Find $m\angle ABD$

Substitute $x = 7$ into the expression for $m\angle ABD$. $m\angle ABD=2x + 23=2\times7+23=14 + 23=37^{\circ}$.

Step4: Find $m\angle DBC$

Substitute $x = 7$ into the expression for $m\angle DBC$. $m\angle DBC=9x - 5=9\times7-5=63 - 5=58^{\circ}$.

Answer:

1. $m\angle LMN=108^{\circ}$
2. $x = 7$, $m\angle ABD = 37^{\circ}$, $m\angle DBC = 58^{\circ}$