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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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!
To find the measure of angle BAC, we need to know that angles in an isosceles triangle are congruent. Therefore, angle BAC is equal to angle ABC. Given that angle ABC is 75°, the measure of angle BAC is also 75°.
The correct answer is D) 75°.