12. (1.30) from the given statement below, select the definition, property, postulate, or theorem that leads to the statement you are asked to prove.
given: $ \overline { a b } = \overline { x y } ; \angle b \cong \angle y ; \overline { c b } \cong \overline { z y } $
prove: $ \delta a b c \cong \delta x y z $
a. definition of congruent triangles
b. angle-angle-side theorem
c. side-angle-side postulate
d. side-side-side postulate
e. angle-side-angle postulate
13. (1.30) from the given statement below, select the
definition, property, postulate, or theorem that
leads to the statement you are asked to prove.
given: $ \angle a \cong \angle x ; \overline { b c } \cong \overline { y z } ; \angle c \cong \angle z $
prove: $ \delta a b c \cong \delta x y z $
a. definition of congruent triangles
b. angle-angle-side theorem
c. side-angle-side postulate
d. side-side-side postulate
e. angle-side-angle postulate
14. (1.31) in $ \delta l m n $, the exterior angle adjacent to $ \angle l $ has a measure of $ 5 x + 12 $.
if $ m \angle m = 3 x - 2 $ and $ m \angle n = 50 $, find the measure of $ \angle l $.
a. 56
b. 78
c. 94
d. 123
e. none of the above
15. (1.10) $ \overrightarrow { v f } $ is between $ \overrightarrow { v a } $ and $ \overrightarrow { v b } $. if $ m \angle a v f = 32, m \angle f v b = 2 x + 9 $, and
$ m \angle a v b = 3 x - 4 $, then find $ m \angle a v b $.
a. 106
b. 97
c. 84
d. 131
e. none of the above
16. (1.16) the measure of an angle is 34 greater than its supplement. find the measures of both angles.
a. 73, 107
b. 24, 128
c. 64, 101
d. 45, 97
e. none of the above

Question

12. (1.30) from the given statement below, select the definition, property, postulate, or theorem that leads to the statement you are asked to prove.
given: $ \overline { a b } = \overline { x y } ; \angle b \cong \angle y ; \overline { c b } \cong \overline { z y } $
prove: $ \delta a b c \cong \delta x y z $
a. definition of congruent triangles
b. angle-angle-side theorem
c. side-angle-side postulate
d. side-side-side postulate
e. angle-side-angle postulate
13. (1.30) from the given statement below, select the
 definition, property, postulate, or theorem that
 leads to the statement you are asked to prove.
given: $ \angle a \cong \angle x ; \overline { b c } \cong \overline { y z } ; \angle c \cong \angle z $
prove: $ \delta a b c \cong \delta x y z $
a. definition of congruent triangles
b. angle-angle-side theorem
c. side-angle-side postulate
d. side-side-side postulate
e. angle-side-angle postulate
14. (1.31) in $ \delta l m n $, the exterior angle adjacent to $ \angle l $ has a measure of $ 5 x + 12 $.
if $ m \angle m = 3 x - 2 $ and $ m \angle n = 50 $, find the measure of $ \angle l $.
a. 56
b. 78
c. 94
d. 123
e. none of the above
15. (1.10) $ \overrightarrow { v f } $ is between $ \overrightarrow { v a } $ and $ \overrightarrow { v b } $. if $ m \angle a v f = 32, m \angle f v b = 2 x + 9 $, and
$ m \angle a v b = 3 x - 4 $, then find $ m \angle a v b $.
a. 106
b. 97
c. 84
d. 131
e. none of the above
16. (1.16) the measure of an angle is 34 greater than its supplement. find the measures of both angles.
a. 73, 107
b. 24, 128
c. 64, 101
d. 45, 97
e. none of the above

Accepted Answer

# Explanation:
## Step1: Use the exterior - angle theorem
The exterior - angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two non - adjacent interior angles.
So, $5x + 12=(3x - 2)+50$.
## Step2: Solve the equation for $x$
$$
\begin{align*}
5x+12&=3x - 2+50\
5x+12&=3x+48\
5x - 3x&=48 - 12\
2x&=36\
x& = 18
\end{align*}
$$
## Step3: Find the measure of $\angle L$
The sum of the interior angles of a triangle is $180^{\circ}$. Let $\angle L=y$. Then $y+(3x - 2)+50 = 180$.
Since $x = 18$, $3x-2=3\times18 - 2=54 - 2 = 52$.
$$
\begin{align*}
y+52 + 50&=180\
y+102&=180\
y&=180-102\
y&=78
\end{align*}
$$

# Answer:
B. 78

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QUESTION IMAGE

Question

Explanation:

Step1: Use the exterior - angle theorem

Step2: Solve the equation for \(x\)

Step3: Find the measure of \(\angle L\)

Answer: