Question

1. (l36) 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. (l36) 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. (l31) 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. (l10) \\( \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. (l16) 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

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 \(x\)

$$
LATEXBLOCK0
$$

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

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle L = y\). Then \(y+(3x - 2)+50 = 180\).
Since \(x = 18\), \(3x-2=3\times18 - 2=54 - 2 = 52\)
\(y+52 + 50=180\)
\(y=180-(52 + 50)=78\)

Answer:

B. 78