Question

M∠LKJ = 153°

m∠LKE = (x + 36)°
m∠EKJ = (x + 105)°
A) 3
B) 4
C) 6
D) 9

Answer 1

C x=6

Explanation:

m∠LKE + m∠EKJ = m∠LKJ → (x + 36) + (x + 105) = 153 → x = 6

Answer 2

C

Explanation:

Angle Addition Postulate describes that putting two angles side by side with their vertices together creates a new angle whose measure equals the sum of the measures of the two original angles.

By Angle Addition Postulate,

`m\angle LKJ=m\angle LKE+m\angle EKJ`

Since

`m\angle LKJ = 153^(\circ)\\ \\m\angle LKE = (x + 36)^(\circ)\\ \\m\angle EKJ = (x + 105)^(\circ),`

you have

`153^(\circ)=(x+36)^(\circ)+(x+105)^(\circ)\\ \\x+36+x+105=153\\ \\2x+141=153\\ \\2x=153-141\\ \\2x=12\\ \\x=6`