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Wittaler [7]
3 years ago
6

The sum of the measures of angles for a triangle is 180°. Find the value of x and then the measures of the 3 angles

Mathematics
1 answer:
dmitriy555 [2]3 years ago
6 0

Answer:

The value of x is 50

The measures of the 3 angles are 50°, 100°, 30°

Step-by-step explanation:

Let us solve the question

∵ The sum of the measures of the angles of a triangle is 180°

∵ The measures of the 3 angles of the given Δ are x°, 2x°, (x - 20)°

→ Add them and equate the sum by 180

∴ x° + 2x° + (x - 20)° = 180°

→ Add the like terms

∵ (x + 2x + x) + (-20) = 180

∴ 4x - 20 = 180

→ Add 20 to both sides

∵ 4x - 20 + 20 = 180 + 20

∴ 4x = 200

→ Divide both sides by 4 to find x

∴ x = 50

∴ The value of x is 50

To find the measures of the 3 angles substitute x by 50 in their expressions

∵ The measure of one angle is x

∴ The measure of the 1st angle is 50°

∵ The measure of the 2nd angle is 2x

∴ The measure of the 2nd angle = 2(50)

∴ The measure of the 2nd angle is 100°

∵ The measure of the 3rd angle is (x - 20)

∴ The measure of the 3rd angle = (50 - 20)

∴ The measure of the 3rd angle is 30°

∴ The measures of the 3 angles are 50°, 100°, 30°

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Complete Question

The complete question is shown on the first uploaded image

Answer:

the null hypothesis is  H_o  :  \mu =  122

the alternative hypothesis is H_a  :  \mu \ne  122

The test statistics is  t =  - 1.761

The p-value is  p =  P(Z  <  t ) = 0.039119

so

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Step-by-step explanation:

From the question we are told that

   The population mean is  \mu  = 122

     The sample size is  n=  38

    The sample mean is  \= x  =  116 \ feet

     The standard deviation is \sigma  =  21

     

Generally the null hypothesis is  H_o  :  \mu =  122

                the alternative hypothesis is H_a  :  \mu \ne  122

Generally the test statistics is mathematically evaluated as

         t =  \frac { \= x - \mu }{\frac{ \sigma }{ \sqrt{n} } }

substituting values

         t =  \frac { 116 -  122 }{\frac{ 21 }{ \sqrt{ 38} } }

         t =  - 1.761

The p-value is mathematically represented as

      p =  P(Z  <  t )

From the z- table  

     p =  P(Z  <  t ) = 0.039119

So  

     p  \ge 0.01

 

         

     

           

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