Question
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?
Answers
GPT 3.5
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.
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.