In the given figure, m ∠AEJ = 55°, m ∠BIC = 130°. Also, AE || BF, CG || DH and AD || JH. BI and CI are the angle bisectors of the ∠CBF and ∠BCG respectively. What is the measure of ∠DHG?
Explanation:
∠BFE and ∠AEJ are corresponding angles.
∴ m ∠BFE = m ∠AEJ = 55°
∠CBF and ∠BFE are alternate angles.
∴ m ∠CBF = m ∠BFE = 55°
∵ BI is the bisector of ∠CBF, we have,
∴ m ∠IBC = (m ∠CBF)/2 = 27.5°
∴ m ∠ICB = 180° − (m ∠BIC + m ∠IBC) = 180° − (130° + 27.5°)= 22.5°
m ∠BCG = 2 × m ∠ICB = 45°
∴ m ∠CGF = 180° − m ∠BCG = 135°
m ∠DHG = m ∠CGF = 135° (∵ m∠DHG and m∠CGF form a pair of Corresponding angles)
Hence, option (b).
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