Question

10 multiple choice 1 point using the given figure, find the length of $overline{tu}$ if $overline{sv}$ is 30 units.
$s$———18———$t$——$u$———$v$
$t$———18———$v$
6 units
3 units
18 units
14 units
11 multiple choice 1 point what is the measure of angle 1 in the figure below?
1 120°
80°
60°
30°
40°

Explanation:

Step1: Identify segment - length relationship

We know that $SV=ST + TU+UV$ and $ST = 18$, $UV = 18$, $SV = 30$.

Step2: Set up the equation

$30=18 + TU+18$.

Step3: Solve for $TU$

$TU=30-(18 + 18)=30 - 36=- 6$ is incorrect. The correct way is $SV=ST + UV - TU$. So $30=18 + 18-TU$, then $TU=18 + 18 - 30=6$.

Step4: Identify angle - relationship for second question

The two angles are supplementary (linear - pair). Let the measure of angle 1 be $x$. Then $x + 120^{\circ}=180^{\circ}$.

Step5: Solve for the measure of angle 1

$x=180^{\circ}-120^{\circ}=60^{\circ}$.

Answer:

1. A. 6 units
2. B. $60^{\circ}$