Question

find the measure of angle 2.

Explanation:

Step1: Identify congruent angles

$\angle 5 = 7x - 62$ (corresponding angles are congruent)

Step2: Set up supplementary angle equation

$\angle 5 + (-4x + 185) = 180$ (linear pair is supplementary)
Substitute $\angle 5$:
$7x - 62 + (-4x + 185) = 180$

Step3: Simplify and solve for $x$

Combine like terms:
$3x + 123 = 180$
Subtract 123:
$3x = 180 - 123 = 57$
Solve for $x$:
$x = \frac{57}{3} = 19$

Step4: Find $\angle 3$, then $\angle 2$

First calculate $\angle 3 = 7x - 62$:
$\angle 3 = 7(19) - 62 = 133 - 62 = 71$
$\angle 2 + \angle 3 = 180$ (linear pair is supplementary)
$\angle 2 = 180 - 71 = 109$

Answer:

$109$