45. In the following figure seg PQ || seg RS and seg EF || seg GH. Find ZMNH.
Kyle
G
(3x + 10%
0
→
T
Q
P
(2x - 25)
N
S
R
M м
TE
JH
(1) 1270
(2) 63°
(3) 530
(4) 117°
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Answer:
A(Δ PQF) = 20units,PF = 2DP,Let us assume DP = x,∴ PF = 2x
⇒ DF = DP + PF = x + 2x = 3x
In Δ FDE & Δ FPQ
∠ FDE ≅ ∠ FPQ (Corresponding angles)
∠ FEP ≅ ∠ FQP (Corresponding angles)
∴ Δ FDE~ Δ FPQ (AA Test)
∴ 
A(Δ FDE) =  A(ΔFPQ) = × 20 = 45
A(□DPQE) = A (Δ FDE) - A(ΔFPQ)
= 45-20
= 25 sq.unit.
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