Question
22. Triangle \( A B C \) is similar to triangle \( D E F \). Angle \( A \) measures \( 70^{\circ} \), angle \( B \) measures \( 50^{\circ} \), and angle \( C \) measures \( 60^{\circ} \). What is the measure of angle \( E \) ? F. \( 70^{\circ} \) G. \( 50^{\circ} \) H. \( 60^{\circ} \) J. \( 180^{\circ} \)
Ask by Pierce Wade. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Angle \( E \) measures \( 50^{\circ} \).
Solution
In similar triangles, corresponding angles are equal. Given that triangle \( ABC \) is similar to triangle \( DEF \), the correspondence of angles is as follows:
- Angle \( A \) corresponds to angle \( D \)
- Angle \( B \) corresponds to angle \( E \)
- Angle \( C \) corresponds to angle \( F \)
Given:
- Angle \( A = 70^{\circ} \)
- Angle \( B = 50^{\circ} \)
- Angle \( C = 60^{\circ} \)
Since angle \( B \) in triangle \( ABC \) corresponds to angle \( E \) in triangle \( DEF \), the measure of angle \( E \) is equal to the measure of angle \( B \).
**Answer:**
G. \( 50^{\circ} \)
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Simplify this solution The Deep Dive
Since triangle \( A B C \) is similar to triangle \( D E F \), their corresponding angles are equal. Thus, the measure of angle \( E \) corresponds to angle \( A \) in triangle \( A B C \), which is \( 70^{\circ} \). So, the answer is \( \text{F. } 70^{\circ} \). To have fun with similar triangles, think of them as siblings who share not just the same style but also the same traits! Just like in a family, if you know one sibling’s angle, you automatically know their look-alike's angle in a similar triangle. So next time you see a pair of triangles, remember – they’re practically two peas in a pod!
