The figure shows that AB=AC=DE=DC, \(<\) BAC = 30, \(<\) PED = 50 and ABC and ABC are congruent. What is the measure of angle \(<\) ABP = x?
B. 15
C. 20
D. 25
E. 30
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The figure shows that AB=AC=DE=DC,
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Max@Math Revolution
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[GMAT math practice question]
The figure shows that AB=AC=DE=DC, \(<\) BAC = 30, \(<\) PED = 50 and ABC and ABC are congruent. What is the measure of angle \(<\) ABP = x?
A. 10
B. 15
C. 20
D. 25
E. 30
The figure shows that AB=AC=DE=DC, \(<\) BAC = 30, \(<\) PED = 50 and ABC and ABC are congruent. What is the measure of angle \(<\) ABP = x?
A. 10
B. 15
C. 20
D. 25
E. 30
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Max@Math Revolution
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- Posts: 3991
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=>
∠ABC = ∠DEC = (180° - 30°) / 2 = 75°.
Then we have ∠BEC = 180° – ( 50° + 75° ) = 55°.
Since exterior ∠BEC of triangle ABE is the sum of non-adjacent interior angles, 30°, and x, we have x + 30° = 55° or x = 25°.
Therefore, D is the correct answer.
Answer: D
∠ABC = ∠DEC = (180° - 30°) / 2 = 75°.
Then we have ∠BEC = 180° – ( 50° + 75° ) = 55°.
Since exterior ∠BEC of triangle ABE is the sum of non-adjacent interior angles, 30°, and x, we have x + 30° = 55° or x = 25°.
Therefore, D is the correct answer.
Answer: D
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