Questions: triangle ABC is similar to triangle FED. What is m angle D? m angle D =

Transcript text: $\triangle ABC \sim \triangle FED$. What is $m \angle D$ ? \[ m \angle D= \]

Solution

Solution Steps

Step 1: Find the measure of angle B

The sum of the angles in triangle ABC is 180°. We are given m∠A = 54° and m∠C = 76°. Therefore, m∠B = 180° - 54° - 76° = 50°.

Step 2: Use the similarity statement to find corresponding angles

We are given that triangle ABC is similar to triangle FED, written as ∆ABC ~ ∆FED. This tells us that ∠A corresponds to ∠F, ∠B corresponds to ∠E, and ∠C corresponds to ∠D.

Step 3: Find the measure of angle D

Since ∠C corresponds to ∠D and m∠C = 76°, then m∠D = 76°.

Final Answer

The measure of angle D is 76°.

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