Question
In ΔFGH, start overline, F, H, end overlineFH is extended through point H to point I, m, angle, H, F, G, equals, left bracket, 3, x, plus, 15, right bracket, degreesm∠HFG=(3x+15)∘, m, angle, G, H, I, equals, left bracket, 6, x, minus, 6, right bracket, degreesm∠GHI=(6x−6)∘, and m, angle, F, G, H, equals, left bracket, x, plus, 1, right bracket, degreesm∠FGH=(x+1)∘. Find m, angle, H, F, G, .m∠HFG.
Answers
GPT 3.5
To find m∠HFG, we can use the angle sum property of a triangle. The sum of the angles in a triangle is always 180 degrees.
m∠HFG + m∠FGH + m∠HGF = 180 degrees
Plugging in the given values, we have:
(3x + 15) + (x + 1) + (x + 1) = 180
Combine like terms:
5x + 17 = 180
Subtract 17 from both sides:
5x = 163
Divide both sides by 5:
x = 32.6
Now we can find m∠HFG by plugging in the value of x:
m∠HFG = 3x + 15 = 3(32.6) + 15 = 97.8 + 15 = 112.8 degrees
Therefore, m∠HFG = 112.8 degrees.
m∠HFG + m∠FGH + m∠HGF = 180 degrees
Plugging in the given values, we have:
(3x + 15) + (x + 1) + (x + 1) = 180
Combine like terms:
5x + 17 = 180
Subtract 17 from both sides:
5x = 163
Divide both sides by 5:
x = 32.6
Now we can find m∠HFG by plugging in the value of x:
m∠HFG = 3x + 15 = 3(32.6) + 15 = 97.8 + 15 = 112.8 degrees
Therefore, m∠HFG = 112.8 degrees.
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.
GPT 3.5
To find the measure of angle P (m∠P), we can use the given information about the angles in triangle NOP.
We know that the sum of angles in a triangle is 180 degrees.
So, we can set up the equation:
m∠N + m∠O + m∠P = 180 degrees
Substituting the given angle measures:
(9x + 2) + (x + 15) + (4x - 5) = 180
Combine like terms:
14x + 12 = 180
Subtract 12 from both sides:
14x = 168
Divide by 14:
x = 12
Now we can find the measure of angle P (m∠P) by substituting x = 12 into the expression:
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.
We know that the sum of angles in a triangle is 180 degrees.
So, we can set up the equation:
m∠N + m∠O + m∠P = 180 degrees
Substituting the given angle measures:
(9x + 2) + (x + 15) + (4x - 5) = 180
Combine like terms:
14x + 12 = 180
Subtract 12 from both sides:
14x = 168
Divide by 14:
x = 12
Now we can find the measure of angle P (m∠P) by substituting x = 12 into the expression:
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.