Question

given the figure below, find the

(6x + 51)°

z°

(7x + 90)°

x=
z=

Explanation:

Step1: Set up equation

$6x + 51=7x + 90$ (vertical - angles are equal)

Step2: Solve for x

$6x-7x=90 - 51$, $-x = 39$, so $x=-39$

Step3: Find z

$z=6x + 51$, substitute $x=-39$: $z=6\times(-39)+51=-234 + 51=-183$ (but angles can't be negative, likely a mis - setup, should use supplementary angles: $6x + 51+7x + 90 = 180$)

Step4: Correct equation and solve for x

$13x+141 = 180$, $13x=180 - 141=39$, $x = 3$

Step5: Find z

$z=6x + 51$, substitute $x = 3$, $z=6\times3+51=18 + 51=69$

Answer:

$x = 3$
$z = 69$