We are given that three of the exterior angle of the n-sided polygon are 50° each two of its interior angle are 127° and 135° and the remaining interior angle are 173 each.

As we know that the sum of all exterior angles of the polygon is 360°. Also, the number of remaining interior angles will be (n - 5).

And, the exterior angle = 180° - the interior angle.

So, according to the question;

$(3 \times 50) + (180-127) + (180 - 135) + (n - 5)\times (180-173) =360$

150 + 53 + 45 + 7(n - 5) = 360

248 + 7n - 35 = 360

213 + 7n = 360

7n = 360 - 213

7n = 147

n = $\frac{147}{7}$

n = 21

Hence, the value of n is 21 and this is a 21-sided polygon.

4 0

3 years ago

Mario’s company makes unusually shaped imitation gemstones. One gemstone has 14 faces and 10 vertices. How many edges does the g

Ivan

The gemstone has 22 edges.

We use Euler's formula on this:

F + V - E = 2

Substituting our information, we have:

14 + 10 - E = 2

Combining like terms,
24 - E = 2

Subtract 24 from both sides:
24 - E - 24 = 2 - 24
-E = -22

Divide both sides by -1:
-E/-1 = -22/-1
E = 22

3 0

2 years ago

Triangle DEF has coordinates D(3, 4), E(4, 1), and F(1, -2). If the triangle is

fenix001 [56]

Answer:

Hello! answer: coordinates of E' are (16, 4)

Step-by-step explanation:

4 × 4 = 16 4 × 1 = 4 therefore the new coordinates are (16, 4)

5 0

2 years ago