Questions: If the exterior angle drawn measures 150°, and the measure of ∠D is twice that of ∠E, find the measure of ∠D. m∠D = m∠E =

If the exterior angle drawn measures 150°, and the measure of ∠D is twice that of ∠E, find the measure of ∠D. m∠D = m∠E =
Transcript text: If the exterior angle drawn measures 150°, and the measure of ∠D is twice that of ∠E, find the measure of ∠D. m∠D = m∠E =
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Solution

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Solution Steps

Step 1: Identify the given information

The problem states that the exterior angle \( \angle DFG \) measures 150°, and the measure of \( \angle D \) is twice that of \( \angle E \).

Step 2: Set up the relationship between the angles

Let the measure of \( \angle E \) be \( x \). Since \( \angle D \) is twice \( \angle E \), the measure of \( \angle D \) is \( 2x \).

Step 3: Use the exterior angle theorem

The exterior angle \( \angle DFG \) is equal to the sum of the two remote interior angles \( \angle D \) and \( \angle E \). Therefore: \[ \angle DFG = \angle D + \angle E \] \[ 150° = 2x + x \] \[ 150° = 3x \]

Step 4: Solve for \( x \)

\[ x = \frac{150°}{3} \] \[ x = 50° \]

Step 5: Find the measures of \( \angle D \) and \( \angle E \)

Since \( x = 50° \): \[ \angle E = 50° \] \[ \angle D = 2x = 2 \times 50° = 100° \]

Final Answer

  • \( \angle D = 100° \)
  • \( \angle E = 50° \)
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