In ΔFGH,
m
∠
F
=
(
6
x
−
14
)
∘
m∠F=(6x−14)
∘
,
m
∠
G
=
(
4
x
−
8
)
∘
m∠G=(4x−8)
∘
, and
m
∠
H
=
(
x
+
15
)
∘
m∠H=(x+15)
∘
. Find
m
∠
F
.
m∠F.
We know that the sum of the angles in a triangle is 180 degrees, so we have:
m∠F + m∠G + m∠H = 180
Substituting in the given angle measures, we get:
(6x-14) + (4x-8) + (x+15) = 180
11x + 3 = 180
Solving for x, we get:
x = 15
Now we can find m∠F:
m∠F = 6x-14 = 6(15) - 14 = 86
Therefore, m∠F is 86 degrees.
To find the measure of ∠F, we need to use the fact that the sum of the angles in a triangle is equal to 180 degrees.
In ΔFGH, we have:
m∠F + m∠G + m∠H = 180
Substituting the given expressions for the angle measures, we have:
(6x - 14) + (4x - 8) + (x + 15) = 180
Now, let's solve for x:
6x - 14 + 4x - 8 + x + 15 = 180
11x - 7 = 180
11x = 187
x = 17
Now, substitute the value of x back into the expression for m∠F:
m∠F = 6x - 14
m∠F = 6(17) - 14
m∠F = 102 - 14
m∠F = 88
Therefore, the measure of ∠F is 88 degrees.