Using what you noticed, find the measures of the four angles at point B in this second diagram. Lines AC and DF are parallel.

The measures of the four angles at B are

m∠EBC = 34°

m∠ABH = 34°

m∠EBA = 146°

m∠CBH = 146°

Step-by-step explanation:

∵ AC // DF

∵ HG is the transversal

∴ m∠GEF = m∠EBC ⇒ corresponding angles

∵ m∠GEF = 34°

∴ m∠EBC = 34°

∵ GH intersects AC at B

∴ m∠EBC = m∠ABH ⇒ vertically opposite angles

∵ m∠EBC = 34°

∴ m∠ABH = 34°

∵ B ∈ AC

∴ ∠EBC and ∠EBA formed a pair of linear angles

∵ The sum of the measures of the pair of linear angles is 180°

∴ m∠EBC + m∠EBA = 180°

→ Substitute m∠EBC by 34°

∴ 34 + m∠EBA = 180

→ Subtract 34 from both sides

∵ 34 - 34 + m∠EBA = 180 - 34

∴ m∠EBA = 146°

∵ ∠EBA and ∠CBH are vertically opposite angles

∴ m∠EBA = m∠CBH

∵ m∠EBA = 146°

∴ m∠CBH = 146°