Given:
m∠F = 54 degrees
Let's solve for m∠G and m∠H.
From the given triangle FGH, we can see the opposite sides are equal.
FG = GH
Since the opposite sides are equal it is an isosceles triangle.
The base angles of an isosceles triangle are congruent.
∠F and ∠H are the base angles.
Thus, we have:
m∠H ≅ m∠F = 54 degrees.
Now, to find m∠G, apply the Triangle Angle Sum Theorem.
The sum of the interior angles in a triangle is 180 degrees.
m∠G + m∠H + m∠F = 180
m∠G + 54 + 54 = 180
m∠G + 108 = 180
Subtract 108 from both sides:
m∠G + 108 - 108 = 180 - 108
m∠G = 72 degrees.
In ΔFGH, m∠F = 54°, m∠G = 72°, m∠H = 54°
ANSWER:
• m∠G = 72°
,
• m∠H = 54°
