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Nata [24]
3 years ago
11

Find the value of x​

Mathematics
2 answers:
damaskus [11]3 years ago
5 0

Answer: x = -14

<u>Step-by-step explanation:</u>

a) Top triangle, top angle: Using the Linear Pair Postulate, 180° - 126° = 54°

b) Top triangle, bottom left angle: Congruent sides implies congruent angles = 54°

c) Bottom triangle, top left angle: Using the Complimentary Angles Postulate, 90° - 54° = 36°

d) Bottom triangle, bottom angle: Congruent sides implies congruent angles = 36°

Triangle Sum Theorem states that the sum of the three angles must equal 180°.

36° + ∠2 + 36° = 180°

36° + (x + 22) + 36° = 180°

x + 194 = 180

         x = -14

soldier1979 [14.2K]3 years ago
3 0

Answer:

x = -14

Step-by-step explanation:

Look at the image attatched. I have labeled the angles for better explanation.

We know that angle 1 is 54 degrees as is rests on a straight line with its adjacent angle at 126 degrees. This means that angle 1 would be 180 - 126 degrees, or 54 degrees. We also know that angle 1 and 3 must be congruent as the sides of the triangle opposite those angles are congruent as well. This means that both those angles are 54 degrees. Since the sum of all angles in a triangle must equal 180 degrees, we can get that angle 4 is 180 - (2*54) degrees, or 72. Since angle two and angle 4 both lie on a straight line, they must add up to 180 degrees. This means that the value of angle 2 would be 180 - 72, or 108 degrees. Since angle 2 is also equal to x+122, we get the equation:

108 = x + 122.

We then solve this by getting:

x = 108 - 122

which gives us the answer of

x = -14

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Answer:

Problem 1:

a. x=2

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Problem 2:

A multiplication equation to hold the table true:

18\times3=54

A division equation to hold the table true:

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Step-by-step explanation:

Given in problem 1:

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It holds true for all values of x> 6.

Let us say x=12,

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(b). The equation is \frac{x}{6} < 1

It holds true for all values of x< 6.

Let us say x=3

\frac{x}{6} =\frac{3}{6} =\frac{1}{2} which is less than 1.

(c). The equation is \frac{x}{6} = 1

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Let us say x=6,

\frac{x}{6} =\frac{6}{6}=1 which is equal to 1.

Problem 2:

A multiplication equation to hold the table true:

18\times3=54

A division equation to hold the table true:

\frac{54}{3} =18

Therefore these are the values which hold true to the equation in problem 1 and 2.

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Step-by-step explanation:

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