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MissTica
3 years ago
14

Find the measure of an interior and an exterior angle of a regular 46-gon

Mathematics
1 answer:
trapecia [35]3 years ago
7 0
For any polygon, the formula of the interior angle is 180 - 360/n where n is the number of sides of the polygon. The exterior angle is the supplementary angle of the interior angle. Hence when n is equal to 46, then interior angle is equal to 172.17 degrees and the exterior is equal to 7.83 degrees. 
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In the adjoining figure, XY = XZ . YQ and ZP are the bisectors of <img src="https://tex.z-dn.net/?f=%20%5Cangle" id="TexFormula1
svetlana [45]

Answer:

See Below.

Step-by-step explanation:

Statements:                                              Reasons:

1)\, XY=XZ                                              Given

2) \text{ $ m\angle Y= m\angle Z$}                                        Isosceles Triangle Theorem

\displaystyle 3) \text{ $m\angle Y=m\angle XYQ + \angle QYZ$}                  Angle Addition

\displaystyle 4)\text{ $YQ$ bisects $\angle XYZ$}                               Given

5) \text{ $m\angle XYQ=m\angle QYZ$}                           Definition of Bisector

\displaystyle 6)\text{ $m\angle Y=2m\angle QYZ$}                               Substitution

7)\text{ $m\angle Z=m\angle XZP+m\angle PZY$}              Angle Addition

8)\text{ $ZP$ bisects $\angle XZY$}                              Given

\displaystyle 9) \text{ $m\angle XZP=m\angle PZY$ }                          Definition of Bisector

\displaystyle 10) \text{ $ m\angle Z = 2m\angle PZY $}                            Substitution

11)\text{ } 2m\angle QYZ=2m\angle PZY                    Substitution

12)\text{ }m\angle QYZ=m\angle PZY                        Division Property of Equality

13)\text{ } YZ=YZ                                         Reflexive Property

14)\text{ } \Delta YZP\cong\Delta ZYQ                             Angle-Side-Angle Congruence*

15)\text{ } YQ=ZP                                         CPCTC

*For clarification:

∠Y = ∠Z

YZ = YZ (or ZY)

∠PZY = ∠QYZ

So, Angle-Side-Angle Congruence:

ΔYZP is congruent to ΔZYQ

5 0
3 years ago
Read 2 more answers
CITY |. Temperature (°F) St. Louis | 32 Montreal |. -18 Buffalo. | -8 Orlando. |. 68 Juneau. |. -26 By noon, the temperature In
Leno4ka [110]

Answer:

6°F

58°F

Step-by-step explanation:

From the data Given :

Temperature rise in Buffalo by noon time = 14°F

The initial temperature at Buffalo = - 8°F

Rise in temperature = 14°F

Therefore, temperature at noon = (-8 + 14)°F = 6°F

B.)

Temperature at 6am in St. Louis = 32°F

Temperature at 6am in Juneau = - 26°F

Temperature difference :

(32 - (-26))°F

32 + 26

= 58°F

Temperature in St. Louis is 58°F higher

8 0
3 years ago
F(x) has domain , and range
marta [7]
Domain: {-4, -2, 0, 2, 4}
range: {-2, -1, 0, 1, 2}
7 0
2 years ago
Farad wrote the expression 32 - 8f to represent
motikmotik
Look at this and you will be surprised on how it helps many like you that’s a key answer

7 0
2 years ago
Read 2 more answers
Need help with these math questions please.
Bas_tet [7]

Answer:

8 - 2π square units.

π/16 - 1/8 square units.

6π - 9√3 square units.

Step-by-step explanation:

The area of the square = 2√2 * 2√2

= 2*2*2

= 8.

The area of the circle = πr^2

= π * [ ( 2√2)/ 2) ]^2

=  π (√2)^2

=  2π.

Second Question:

The area of the circle = π(1/2)^2 = π/4.

Finding the area of the square:

1^2 = 2x^2

x^2 = 1/2

So the area of the square = 1/2

So the area of the red part = 1/4 ( π/4 - 1/2).

= π/16 - 1/8.

Third question

Area of the circle = 6^2 * π = 36π.

Now 60 degrees is 1/6 of 360 degrees so the are of the sector is 6π.

The area of the segment = 6π -  0.5 * 6^2 sin 60

= 6π - 18√3/2

= 6π - 9√3 square units.

6 0
2 years ago
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