In ΔFGH,

Question

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.

Answer 1

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.