In ΔPQR, m, angle, P, equals, left bracket, 4, x, plus, 14, right bracket, degreesm∠P=(4x+14)∘, m, angle, Q, equals, left bracket, x, plus, 16, right bracket, degreesm∠Q=(x+16)∘, and m, angle, R, equals, left bracket, 3, x, minus, 2, right bracket, degreesm∠R=(3x−2)∘. What is the value of x, question markx?
Since the sum of the angles in a triangle is always 180 degrees, we have the equation:
(4x + 14) + (x + 16) + (3x - 2) = 180
Combining like terms, we get:
8x + 28 = 180
Subtracting 28 from both sides, we have:
8x = 152
Dividing both sides by 8, we get:
x = 19
So the value of x is 19.
To find the value of x, we can use the fact that the sum of angles in a triangle is always 180 degrees.
In triangle PQR, the sum of the three angles is equal to 180 degrees:
m∠P + m∠Q + m∠R = 180
Substituting the given angle measures:
(4x + 14) + (x + 16) + (3x - 2) = 180
Combine like terms:
4x + x + 3x + 14 + 16 - 2 = 180
8x + 28 = 180
Subtract 28 from both sides of the equation:
8x = 180 - 28
8x = 152
Divide both sides by 8:
x = 152 / 8
x = 19
Therefore, the value of x is 19.
To find the value of x in the given problem, we need to use the fact that the sum of angles in a triangle is equal to 180 degrees.
We have the following information:
m∠P = 4x + 14
m∠Q = x + 16
m∠R = 3x - 2
According to the triangle angle sum property, we have the equation:
m∠P + m∠Q + m∠R = 180
Substituting the given expressions for the angle measures, we get:
(4x + 14) + (x + 16) + (3x - 2) = 180
Now, let's solve for x:
Combine like terms:
4x + x + 3x + 14 + 16 - 2 = 180
8x + 28 = 180
Subtract 28 from both sides:
8x = 152
Divide both sides by 8:
x = 152/8
Simplifying:
x = 19
Therefore, the value of x is 19.