Question

review & refresh
in exercises 55–57, find the value of ( x ).
55.
triangle with angles ( x^circ ), ( 76^circ ), ( 41^circ )
56.
two parallel lines cut by a transversal, with angles ( (8x - 16)^circ ) and ( (3x + 20)^circ ) shown

Explanation:

Step1: Sum triangle angles to 180°

$x + 76 + 41 = 180$

Step2: Simplify left side

$x + 117 = 180$

Step3: Solve for x (Exercise 55)

$x = 180 - 117 = 63$

Step4: Set angles equal (alternate interior)

$8x - 16 = 3x + 20$

Step5: Isolate x terms

$8x - 3x = 20 + 16$

Step6: Simplify and solve for x (Exercise 56)

$5x = 36 \implies x = \frac{36}{5} = 7.2$

Answer:

Exercise 55: $x = 63$
Exercise 56: $x = 7.2$ (or $\frac{36}{5}$)