In ΔNOP, m, angle, N, equals, left bracket, 9, x, plus, 2, right bracket, degreesm∠N=(9x+2)∘, m, angle, O, equals, left bracket, x, plus, 15, right bracket, degreesm∠O=(x+15)∘, and m, angle, P, equals, left bracket, 4, x, minus, 5, right bracket, degreesm∠P=(4x−5)∘. Find m, angle, P, .m∠P.
To find the measure of angle P (m∠P), we need to set up an equation using the given information.
According to the Angle Sum Property of a triangle, the sum of the measures of the angles in a triangle is always 180 degrees.
Therefore, we have the equation:
m∠N + m∠O + m∠P = 180 degrees
Plug in the given expressions for the angle measures:
(9x + 2) + (x + 15) + (4x - 5) = 180
Combine like terms:
14x + 12 = 180
Subtract 12 from both sides:
14x = 168
Divide both sides by 14:
x = 12
Now substitute the value of x back into the expression for m∠P:
m∠P = 4x - 5 = 4(12) - 5 = 48 - 5 = 43 degrees
Therefore, the measure of angle P (m∠P) is 43 degrees.
To find the measure of angle P (m∠P), we need to solve the equation for angle P.
Given:
m∠N = (9x + 2)°
m∠O = (x + 15)°
m∠P = (4x - 5)°
To find the value of x, we can use the fact that the sum of the angles in a triangle is 180°.
m∠N + m∠O + m∠P = 180°
Substituting the given angle measures:
(9x + 2)° + (x + 15)° + (4x - 5)° = 180°
Combining like terms:
14x + 12 = 180
Subtracting 12 from both sides:
14x = 168
Dividing both sides by 14:
x = 12
Now that we have the value of x, we can find the measure of angle P (m∠P) by substituting x = 12 into the equation for m∠P:
m∠P = (4x - 5)°
m∠P = (4 * 12 - 5)°
m∠P = (48 - 5)°
m∠P = 43°
Therefore, the measure of angle P is 43° (m∠P = 43°).
To find the measure of angle P (m∠P), we need to use the angle sum property of triangles. According to this property, the sum of the measures of the angles in any triangle is always 180 degrees.
In triangle ΔNOP, we have:
m∠N = 9x + 2 degrees
m∠O = x + 15 degrees
m∠P = 4x - 5 degrees
Using the angle sum property, we can write the equation:
m∠N + m∠O + m∠P = 180
Substituting the given angle measures, we get:
(9x + 2) + (x + 15) + (4x - 5) = 180
Simplifying the equation:
14x + 12 = 180
Subtracting 12 from both sides:
14x = 168
Dividing both sides by 14:
x = 12
Now that we know the value of x, we can find m∠P by substituting it back into the equation:
m∠P = 4x - 5
m∠P = 4(12) - 5
m∠P = 48 - 5
m∠P = 43 degrees
Therefore, the measure of angle P (m∠P) is 43 degrees.