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ch4aika [34]
3 years ago
10

In the figure M angle 11=62 and M angle 14=38 find the measure of each angle. tell which postulate or theorems you used

Mathematics
2 answers:
artcher [175]3 years ago
7 0

We are given

angle(11)=62

angle(14)=38

Calculation of angle(1):

we know that

angle(1) and angle(9) are corresponding angles

so,

angle(1)=angle(9)

and angle(9) and angle(14) are vertically opposite angles

so, angle(9)=angle(14)=38

so, angle(1)=angle(9)=angle(14)=38

angle(1)=38

angle(9)=38

Calculation of angle(3):

we know that angle(3) and angle(8) are corresponding angles

so, angle(3)=angle(8)

and angle(8) and angle(11) are vertically opposite angles

so,

angle(3)=angle(8)=angle(11)=62

so,

angle(3)=62

angle(8)=62

Calculation of angle(2):

we know that

angle(1) , angle(2) and angle(3) form supplementary angles

so,

angle(1) + angle(2)+angle(3)=180

we can plug values

38 + angle(2)+62=180

angle(2)=80

Calculation of angle(4):

Since, angle(4) and angle(3) are vertically opposite angles

so,

angle(4)=angle(3)=62

so,

angle(4)=62

Calculation of angle(5):

Since, angle(5) and angle(2) are vertically opposite angles

so,

angle(5)=angle(2)=80

so,

angle(5)=80

Calculation of angle(6):

Since, angle(6) and angle(1) are vertically opposite angles

so,

angle(6)=angle(1)=38

so,

angle(6)=38

Calculation of angle(7):

Since, angle(7) and angle(8) are supplementary angles

so, angle(7)+angle(8)=180

angle(8)=62

angle(7)+62=180

angle(7)=118

Calculation of angle(10):

Since, angle(9) and angle(10) are supplementary angles

so, angle(9)+angle(10)=180

angle(9)=38

angle(10)+38=180

angle(10)=142

Calculation of angle(12):

Since, angle(7) and angle(12) are vertically opposite angles

so,

angle(7)=angle(12)=118

angle(12)=118

Calculation of angle(13):

Since, angle(10) and angle(13) are vertically opposite angles

so,

angle(10)=angle(13)=142

angle(13)=142

So, our angles are

angle(1)=38

angle(2)=80

angle(3)=62

angle(4)=62

angle(5)=80

angle(6)=38

angle(7)=118

angle(8)=62

angle(9)=38

angle(10)=142

angle(11)=62

angle(12)=118

angle(13)=142

angle(14)=38..............Answer



Tcecarenko [31]3 years ago
4 0

from the given figure two lines are parallel to each other. If ∠11=62 then ∠12 =(180- 62)=118,∠8=62 (vertically opposite angles are parallel) and ∠4=62 corresponding angles are equal )If ∠8=62 then ∠3=62 (corresponding angles in a parallel lines are equal)\\  If ∠14=38 then∠13=(180-38)=142 , ∠6=38 (corresponding angles) and ∠9=38 (vertically opposite angles).\\ If ∠6=38 then∠1=38 (vertically opposite angles)\\ If ∠1=38 and ∠3=62 then ∠2=180-(38+62)=80 and if ∠2=80 then ∠5=80 (vertically opposite angles)  

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General Formulas and Concepts:

<u>Calculus</u>

Limits

  • Right-Side Limit:                                                                                             \displaystyle  \lim_{x \to c^+} f(x)
  • Left-Side Limit:                                                                                               \displaystyle  \lim_{x \to c^-} f(x)

Limit Rule [Variable Direct Substitution]:                                                             \displaystyle \lim_{x \to c} x = c

Limit Property [Addition/Subtraction]:                                                                   \displaystyle \lim_{x \to c} [f(x) \pm g(x)] =  \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)

Step-by-step explanation:

*Note:

In order for a limit to exist, the right-side and left-side limits must equal each other.

<u>Step 1: Define</u>

<em>Identify</em>

\displaystyle f(x) = \left\{\begin{array}{ccc}5 - x,\ x < 5\\8,\ x = 5\\x + 3,\ x > 5\end{array}

<u>Step 2: Find Right-Side Limit</u>

  1. Substitute in function [Limit]:                                                                         \displaystyle  \lim_{x \to 5^+} 5 - x
  2. Evaluate limit [Limit Rule - Variable Direct Substitution]:                           \displaystyle  \lim_{x \to 5^+} 5 - x = 5 - 5 = 0

<u>Step 3: Find Left-Side Limit</u>

  1. Substitute in function [Limit]:                                                                         \displaystyle  \lim_{x \to 5^-} x + 3
  2. Evaluate limit [Limit Rule - Variable Direct Substitution]:                           \displaystyle  \lim_{x \to 5^+} x + 3 = 5 + 3 = 8

∴ Since  \displaystyle \lim_{x \to 5^+} f(x) \neq \lim_{x \to 5^-} f(x)  , then  \displaystyle \lim_{x \to 5} f(x) = DNE

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit:  Limits

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