Question

in the diagram below, m∠cih = 104° and m∠bgd = 41°. find m∠ahf.
step angle reason
1 m∠cih = 104° given
2 m∠bgd = 41° given
try m∠□ = □° select a reason
(diagram with points e, c, i, g, b, d, h, a, f; angles 104° at i, 41° at g)
you may assume lines that appear straight are straight, but the figure is not otherwise drawn to scale.

Explanation:

Step1: Find vertical angle of ∠CIH

∠CIH and ∠FIE are vertical angles, so m∠FIE = 104°.

Step2: Find vertical angle of ∠BGD

∠BGD and ∠AGH are vertical angles, so m∠AGH = 41°.

Step3: Calculate m∠AHF

∠AHF is an exterior angle of △AGH, equal to the sum of non-adjacent interior angles: m∠AHF = m∠FIE - m∠AGH = 104° - 41° = 63°.

Answer:

63°