Question

NEED HELP WITH GEOMETRY!!!



1. What is the sum of the exterior angles of a convex polygon?

A. 360. <-----my choice

B. 180(n – 2)

C. 180

D. 360n

2. What is the measure of each exterior angle in a regular 10-sided polygon?

18°

180°

360°

36° <-----my choice


3. If each exterior angle or a regular polygon measures 15°, how many sides does the polygon have?

A. 20

B. 22

C. 24 <-----my choice

D. 26

4. The exterior angles of a triangle measure x°, (2x)°, and (3x)°. What is the value of x?

A. 60<-----my choice

B. 72

C. 30

D. 45

5. The exterior angles of an octagon are 42°, 55°, 39°, 20°, 62°, 45°, and 47°. What is the measure of the eighth exterior angle? Show equations and all work that leads to your answer.

360 = 42 + 55 + 39 + 20 + 62 + 45 + 47 + x
360 = 310 + x

360 - 310 = 310 - 310 + x

50 = x

x = 50

Answer 1

You got all of them correct!! Nice job :)

Answer 2

Answer:

Part 1) Option A $360\°$

Part 2) $36\°$

Part 3) Option C $24\°$

Part 4) option A $60\°$

Part 5) $50\°$

Step-by-step explanation:

Part 1) What is the sum of the exterior angles of a convex polygon?

we know that

The Exterior Angle Sum Theorem states that the exterior angles of any polygon will always add up to $360$ degrees

therefore

the answer part 1) is $360\°$

Part 2) What is the measure of each exterior angle in a regular $10$-sided polygon?

we know that

The sum of the exterior angles of any polygon will always add up to $360$ degrees

Let

x-----> the measure of each exterior angle in a regular $10$-sided polygon

we have that

$10x=360\°$

solve for x

$x=360\°/10$

$x=36\°$

Part 3) If each exterior angle or a regular polygon measures $15\°$, how many sides does the polygon have?

Let

x-----> the number of sides of the polygon

we have that

$15\°x=360\°$

solve for x

$x=360\°/15\°$

$x=24\°$

Part 4) The exterior angles of a triangle measure x°, (2x)°, and (3x)°. What is the value of x?

Remember that

The sum of the exterior angles of any polygon will always add up to $360$ degrees

so

$x\°+2x\°+3x\°=360\°$

solve for x

$6x\°=360\°$

$x=360\°/6$

$x=60\°$

Part 5) The exterior angles of an octagon are 42°, 55°, 39°, 20°, 62°, 45°, and 47°. What is the measure of the eighth exterior angle?

Let

x-----> the measure of the eight exterior angle of the octagon

Remember that

The sum of the exterior angles of any polygon will always add up to $360$ degrees

we have that

$42\°+55\°+39\°+20\°+62\°+45\°+47\°+x\°=360\°$

solve for x

$310\°+x\°=360\°$

$x=360\°-310\°$

$x=50\°$