Question

question 7 (2 points)
the expressions (3x+63)° and (7x-45)° represent the measures of two angles of a regular decagon. find the measure of one angle of the decagon.
x =
angle measure = °
blank 1:
blank 2:

Explanation:

Step1: Set angles equal (regular decagon angles are equal)

Since a regular decagon has all interior angles equal, we set the two angle expressions equal:
$3x + 63 = 7x - 45$

Step2: Solve for \( x \)

Subtract \( 3x \) from both sides:
$63 = 4x - 45$

Add 45 to both sides:
$108 = 4x$

Divide by 4:
$x = \frac{108}{4} = 27$

Step3: Find angle measure (substitute \( x = 27 \))

Use either angle expression. Let’s use \( 3x + 63 \):
$3(27) + 63 = 81 + 63 = 144$

Answer:

Blank 1: \( 27 \)
Blank 2: \( 144 \)