Question

1. ∠j and ∠m are base angles of isosceles trapezoid jklm. if ( mangle j = 17x + 7 ), and ( mangle m = 14x + 10 ), find ( mangle k ).

a. 1
b. 78
c. 156
d. 24

Explanation:

Step1: Set angles equal (base angles)

$17x + 7 = 14x + 10$

Step2: Solve for x

$17x - 14x = 10 - 7$
$3x = 3$
$x = 1$

Step3: Calculate $m\angle J$

$m\angle J = 17(1) + 7 = 24$

Step4: Find $m\angle K$ (consecutive angles)

$m\angle K = 180 - 24 = 156$

Answer:

C. 156