High School

After Koji names the angles, he needs to input the angle measurements into the code as well.

- AE bisects ∠CAF.
- AG bisects ∠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.

Determine the measure of each angle.

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°

Learn more about angle measurements here:

https://brainly.com/question/31186705

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