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IF BC=45 find the measure of angle ABD
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05 Mar 2024, 00:55
05 Mar 2024, 00:55
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IF \(\widehat{BC}=45\)° find the measure of angle \(\angle ABD\)
GRE circle and angle.jpg [ 18.1 KiB | Viewed 399 times ]
A. 22.5
B. 45
C. 120
D. 67.5
E. Cannot be determined
Attachment:
GRE circle and angle.jpg [ 18.1 KiB | Viewed 399 times ]
A. 22.5
B. 45
C. 120
D. 67.5
E. Cannot be determined
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Free Materials for the GRE General Exam - Where to get it!!
GRE Geometry Formulas
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Free Materials for the GRE General Exam - Where to get it!!
GRE Geometry Formulas
GRE - Math Book
Re: IF BC=45 find the measure of angle ABD
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07 Apr 2024, 03:33
07 Apr 2024, 03:33
Expert Reply
D.
This problem tests your understanding of the relationship between a circle and an inscribed triangle.AABC is a right triangle. You are also given the chord length BC = 45°. From this you know that the inscribed angle BAC = 22.5°. The diagram shows angle ABC = 90° so you can find angle ACB with:
angle ACB = 180° - angle ABC - angle BAC = 180° - 90° - 22.5°= 67.5°
Next, the diagram shows chord BD is perpendicular to AC so you can use the properties of similar right triangles to show that angle ABD = angle ACB = 67.5°.
The correct answer is D.
This problem tests your understanding of the relationship between a circle and an inscribed triangle.AABC is a right triangle. You are also given the chord length BC = 45°. From this you know that the inscribed angle BAC = 22.5°. The diagram shows angle ABC = 90° so you can find angle ACB with:
angle ACB = 180° - angle ABC - angle BAC = 180° - 90° - 22.5°= 67.5°
Next, the diagram shows chord BD is perpendicular to AC so you can use the properties of similar right triangles to show that angle ABD = angle ACB = 67.5°.
The correct answer is D.
gmatclubot
Re: IF BC=45 find the measure of angle ABD [#permalink]
07 Apr 2024, 03:33
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