Answer :
Final answer:
To determine the measure of each angle, we can assign variables to the unknown angles and set up equations based on the given information. Solving these equations, we find that m∠CAE = 36.4°, m∠CAF = 18.2°, m∠FAH = 73°, m∠GAF = 71.8°, and m∠BAH = 37.4°.
Explanation:
To determine the measure of each angle, we need to use the information given in the question:
- AE bisects angle CAF.
- E1 D AG bisects angle FAH.
- AC is perpendicular to AB.
- m∠BAH is one degree larger than m∠CAE.
- m∠GAF is one degree less than twice m∠CAE.
Let's assign variables to the unknown angles:
- m∠CAE = x
- m∠CAF = m∠EAF = x/2 (since AE bisects angle CAF)
- m∠FAH = m∠E1DA = (2x) + 1 (since E1DAG bisects angle FAH)
- m∠GAF = (2x) - 1 (since m∠GAF is one degree less than twice m∠CAE)
- m∠BAH = x + 1 (since m∠BAH is one degree larger than m∠CAE)
Now, we can set up equations to solve for x:
- x + m∠EAF + m∠GAF = 180° (by the angle sum property of a triangle)
- x/2 + (2x) - 1 + (2x) - 1 = 180°
- 5x - 2 = 180°
- 5x = 182°
- x = 36.4°
Using these values, we can determine the measure of each angle:
- m∠CAE = 36.4°
- m∠CAF = m∠EAF = 18.2°
- m∠FAH = m∠E1DA = 73°
- m∠GAF = 71.8°
- m∠BAH = 37.4°
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