Question

classify each angle as right, acute, or obtuse. then use a protractor to measure the angle to the nearest degree.

1. ∠uzw
2. ∠yzw
3. ∠tzw
4. ∠uzt

algebra in the figure, (overrightarrow{cb}) and (overrightarrow{cd}) are opposite rays, (overrightarrow{ce}) bisects ∠dcf, and (overrightarrow{cg}) bisects ∠fcb.

1. if (mangle dce = 4x + 15) and (mangle ecf=6x - 5), find (mangle dce).
2. if (mangle fcg = 9x + 3) and (mangle gcb = 13x - 9), find (mangle gcb).
3. traffic signs the diagram shows a sign used to warn drivers of a school zone or crossing. measure and classify each numbered angle.

Explanation:

Step1: Use angle - bisector property for question 15

Since $\overrightarrow{CE}$ bisects $\angle DCF$ and $\overrightarrow{CG}$ bisects $\angle FCB$, we know that $\angle DCE=\angle ECF$ and $\angle FCG = \angle GCB$. Given $\angle DCE=4x + 15$ and $\angle ECF=6x-5$. Set up the equation $4x + 15=6x - 5$.
$4x+15 = 6x - 5$
$15 + 5=6x - 4x$
$20 = 2x$
$x = 10$.
Then $\angle DCE=4x + 15=4\times10+15=40 + 15=55^{\circ}$.

Step2: Use angle - addition property for question 16

Given $\angle FCG=9x + 8$ and $\angle GCB=13x-9$. Since $\angle FCB=\angle FCG+\angle GCB$ and $\angle FCG=\angle GCB$ (because $\overrightarrow{CG}$ bisects $\angle FCB$), we set up the equation $9x + 8=13x-9$.
$9x+8 = 13x - 9$
$8 + 9=13x - 9x$
$17 = 4x$
$x=\frac{17}{4}=4.25$.
$\angle GCB=13x-9=13\times4.25-9=55.25 - 9 = 46.25^{\circ}$.

Answer:

For question 15: $\angle DCE = 55^{\circ}$
For question 16: $\angle GCB=46.25^{\circ}$