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Gyzmo Gyzmo · Answer 1 · 2020-10-08T00:09:23+02:00

Answer:

x = 21

Step-by-step explanation:

By the corresponding angle theorem, we can find that the measure of the smaller angle made by transversal and m is 54°.

Using the vertical angle theorem, we can find that the missing angle is the triangle, the two known angles are 4x and 2x, is also 54°.

Since the sum of the interior angles of a triangle is always equal to 180°, we can make the equation:

2x + 4x + 54 = 180

Now we solve for x. Subtract 54 from both sides and combine like terms.

6x = 126

Divide both sides by 6.

x = 21

and now we have found the value of x. x = 21.

I hope you find my answer and explanation to be helpful. Happy studying.

elcharly64 elcharly64 · Answer 2 · 2020-10-08T01:15:58+02:00

Answer:

x=21°

Step-by-step explanation:

Relations Between Angles

We need to recall two basic relations:

* Two angles opposite by crossing lines are always equal.

* The sum of angles in a triangle is 180°

We'll add some variables to the image, so x is easier found. Please check the image below.

The angles U and 54° are opposite and they must be equal, thus U=54°

Since m and n are parallel and they are crossed by a line, the angles V and U are equal, thus V=54°

Finally, The sum of the angles inside the triangle RST must be equal to 180°:

2x+4x+54=180

Joining like terms:

6x=180-54=126

Solving:

x=126/6

x=21°