Asked by D4VD
Calculating Angle Measures
Examine the diagram. It is not drawn to scale.
A triangle has angles 28 degrees, A, C. The exterior angle to the angle with a measure of 28 degrees is D, the exterior angle to angle A is B, the exterior angle to angle C is 125 degrees.
Choose the equation that cannot be used to find the measure of angle B.
m∠B = m∠C + 28°.
m∠B = 360° – (m∠D + 125°).
m∠B = 180° – m∠A.
m∠B = m∠D + 125°.
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Answered by
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m∠B = m∠D + 125°.
Reason: B is an exterior angle at A so B = 28° + C (exterior-angle theorem), B = 180° − A (linear pair), and since D + B + 125° = 360° (sum of the three exterior angles), B = 360° − (D + 125°). But D + 125° = B + 2A (because D = A + C and 125° = 28° + A), so D + 125° = B only if A = 0°, which is impossible. Thus m∠B ≠ m∠D + 125°.
Reason: B is an exterior angle at A so B = 28° + C (exterior-angle theorem), B = 180° − A (linear pair), and since D + B + 125° = 360° (sum of the three exterior angles), B = 360° − (D + 125°). But D + 125° = B + 2A (because D = A + C and 125° = 28° + A), so D + 125° = B only if A = 0°, which is impossible. Thus m∠B ≠ m∠D + 125°.
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