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.

Answer 1

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.

Answer 2

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.

Answer 3

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.