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We appreciate your visit to 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. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

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:

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