First, the angles of triangle MNP add up to 180º. Since angle M is 142º and angle P is 24º, angle N must be (180-24-142)º or 14º.
Now angle N is congruent to angle U.
2x - 50 = 14
2x = 64
x = 32
Segment NP is congruent to segment US, so 13 = 2x - y AND x=32.
13 = 62 - y
y = 49
The perimeter of the regular polygon is 70 inches
<h3>How to determine the perimeter of the regular polygon?</h3>
The sides of the regular polygon is given as:
Side = 10 in
The regular polygon has 7 sides
So, the perimeter of the polygon is calculated as:
P = Side lengths * Number of sides
This gives
P = 10 inches * 7
Evaluate
P = 70 inches
Hence, the perimeter of the regular polygon is 70 inches
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ANSWER
EXPLANATION
The explicit rule for an arithmetic sequence is given by:
It was given that:
and
The common difference is
We plug in the values into the explicit formula to get,
Expand to get,
The explicit rule is
Step-by-step explanation:
Kim: 25
Stacy: t
Total: 57
Equation:
25+t=57
solve for t
t=57-32=32
Stacy made 32 necklaces