Question

find the value of the variable that results in congruent triangles.
15.
(above two triangles: one triangle has a side of 2 in., a side of (3x + 26) in., and an angle of 30°; the other triangle has a side of 2 in., a side of (x + 10) in., and an angle of 30°)
16.
(above two triangles: one triangle has a side of 4 m, a side of 2 m, and an angle of (2x + 8)°; the other triangle has a side of 4 m, a side of 2 m, and an angle of (3.5x - 19)°)

Explanation:

Step1: Set congruent sides equal (Q15)

$3x + 26 = x + 10$

Step2: Solve for x (Q15)

$3x - x = 10 - 26$
$2x = -16$
$x = \frac{-16}{2} = -8$

Step3: Set congruent angles equal (Q16)

$2x + 8 = 3.5x - 19$

Step4: Solve for x (Q16)

$8 + 19 = 3.5x - 2x$
$27 = 1.5x$
$x = \frac{27}{1.5} = 18$

Answer:

For problem 15: $x = -8$
For problem 16: $x = 18$