CPM Homework Help : CCG Problem 9-23

For each geometric relationship represented below, write and solve an equation for $x$ . Show all work.

Hint (a):

What is the sum of the interior angles of a pentagon?
How can you use this to find $x$ ?

Answer (a):

$x = 31^\circ$ , because
$(2x) + (4x − 3) + (7x − 6) + (3x + 12) + (x + 10) = 540^\circ$

Hint (b):

What is the relationship between these two angles?
Is there an angle that both $4x + 20^\circ\text{ and }5x + 2^\circ$ have a geometric relationship to?

Answer (b):

$4x+20^\circ+5x-2^\circ=180^\circ$

$x=18^\circ$