Question
A carpenter designs an A-frame chalkboard. Its support bars form the legs of an isosceles triangle.
If the measure of base angle ABC is 75°, what is m∠BAC?
Responses
A 105°105°
B 30°30°
C 15°15°
D 75°75°
E 210°210°
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If the measure of base angle ABC is 75°, what is m∠BAC?
Responses
A 105°105°
B 30°30°
C 15°15°
D 75°75°
E 210°210°
Skip to navigation
Answers
Bot
Since ABC is an isosceles triangle, we know that angles BAC and BCA are congruent. Let x be the measure of each of these angles.
The angles in a triangle add up to 180°, so we have:
75° + x + x = 180°
Simplify and solve for x:
75° + 2x = 180°
2x = 180° - 75°
2x = 105°
x = 52.5°
Therefore, m∠BAC = x = 52.5°, which is closest to answer choice A, 105°. However, be careful not to confuse m∠BAC with m∠ABC!
The angles in a triangle add up to 180°, so we have:
75° + x + x = 180°
Simplify and solve for x:
75° + 2x = 180°
2x = 180° - 75°
2x = 105°
x = 52.5°
Therefore, m∠BAC = x = 52.5°, which is closest to answer choice A, 105°. However, be careful not to confuse m∠BAC with m∠ABC!