Answer/Step-by-step explanation:
1. An isosceles ∆ has two equal sides. The base angles of an isosceles ∆ are also equal.
Therefore:
m<U = 54° (base angle of isosceles ∆)
m<T = 180 - (54 + 54) (sum of ∆)
m<T = 72°
2. ∆LMN is an isosceles ∆, therefore:
m<M = ½*(180 - 28) = 76°
m<N = m<M (base angle of isosceles)
m<N = 76°
3. ∆FEG is an isosceles ∆, because it has two equal base angles.
Therefore:
EF = FG
EF = 18 in
m<F = 180 - (23 + 23) = 134°
4. ∆PQR is an equilateral ∆. All sides and angles of an equilateral ∆ are equal.
Therefore:
m<P = 60°
m<Q = 60°
m<R = 60°
5. 4x + 23 = 10x - 1 (2 asides of an isosceles ∆ are equal)
Collect like terms
4x - 10x = -23 - 1
-6x = -24
Divide both sides by -6
x = 4
6. 2*(9x - 25) = 180 - 104 (base angles of isosceles ∆)
18x - 50 = 76
Add 50 to both sides
18x = 76 + 50
18x = 126
Divide both sides by 18
x = 7
7. 5x - 7 = 8x - 55 (base angles of an isosceles)
Collect like terms
5x - 8x = 7 - 55
-3x = -48
Divide both sides by -3
x = 16
8. 4x + 8 = 60° (angle of an equilateral ∆)
Subtract 8 from each side
4x = 60 - 8
4x = 52
Divide both sides by 4
x = 13
