Question

the ratio of total interior angles to total exterior angles of a quadrilateral is
select one:
a. 3:1
b. 2:1
c. 1:1
d. 1:2

the sum of the interior angles of a certain polygon is the same as the sum of its exterior angles. how many sides does the polygon have?
select one:
a. 6
b. 10
c. 8
d. 4

Explanation:

Step1: Find total interior angles (quadrilateral)

Sum of interior angles of an $n$-sided polygon: $(n-2)\times180^\circ$. For quadrilateral $n=4$:
$$(4-2)\times180^\circ = 360^\circ$$

Step2: Find total exterior angles

Sum of exterior angles of any polygon is always $360^\circ$.

Step3: Calculate the ratio

Ratio = $\frac{\text{Total interior angles}}{\text{Total exterior angles}} = \frac{360^\circ}{360^\circ} = 1:1$

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Step4: Set up equation for second question

Let $n$ = number of sides. Set interior sum equal to exterior sum ($360^\circ$):
$$(n-2)\times180^\circ = 360^\circ$$

Step5: Solve for $n$

Divide both sides by $180^\circ$:
$$n-2 = 2$$
Add 2 to both sides:
$$n = 4$$

Answer:

1. c. 1:1
2. d. 4