In ΔVWX, start overline, V, X, end overlineVX is extended through point X to point Y, m, angle, X, V, W, equals, left bracket, 3, x, plus, 14, right bracket, degreesm∠XVW=(3x+14)∘, m, angle, V, W, X, equals, left bracket, x, plus, 18, right bracket, degreesm∠VWX=(x+18)∘, and m, angle, W, X, Y, equals, left bracket, 8, x, plus, 8, right bracket, degreesm∠WXY=(8x+8)∘. What is the value of x, question markx?
To find the value of x, we need to set up an equation using the given angle measurements.
First, we know that the sum of the angles in a triangle is 180 degrees. Therefore, we can write the equation:
m∠XVW + m∠VWX + m∠WXY = 180
Substituting the given angle measurements, we have:
(3x+14) + (x+18) + (8x+8) = 180
Now we can solve for x:
3x + 14 + x + 18 + 8x + 8 = 180
12x + 40 = 180
Subtracting 40 from both sides:
12x = 140
Dividing both sides by 12:
x = 11.67
Therefore, the value of x is approximately 11.67.
To find the value of x in the given scenario, we will use the information about the angles in the triangle ΔVWX.
We know that the sum of angles in a triangle is 180 degrees.
In ΔVWX, we have:
m∠XVW = (3x + 14)°
m∠VWX = (x + 18)°
m∠WXY = (8x + 8)°
Using the sum of angles in a triangle, we can write the equation:
(3x + 14) + (x + 18) + (8x + 8) = 180
Simplifying the equation, we get:
3x + 14 + x + 18 + 8x + 8 = 180
12x + 40 = 180
12x = 180 - 40
12x = 140
x = 140/12
x = 11.67 (rounded to two decimal places)
Therefore, the value of x is approximately 11.67.
To find the value of x, we can use the information given about the angles in the triangle ΔVWX.
We are given the following equations:
m∠XVW = (3x + 14)°
m∠VWX = (x + 18)°
m∠WXY = (8x + 8)°
Since all angles in a triangle sum up to 180°, we can set up an equation:
m∠XVW + m∠VWX + m∠WXY = 180°
Substituting the given equations into this equation, we get:
(3x + 14) + (x + 18) + (8x + 8) = 180
Simplifying the equation:
3x + 14 + x + 18 + 8x + 8 = 180
Combining like terms:
12x + 40 = 180
Subtracting 40 from both sides:
12x = 140
Dividing both sides by 12:
x = 140/12
Simplifying the fraction:
x = 35/3
Therefore, the value of x is 35/3.