Question

Triangle A B C is shown with its exterior angles. Line C B extends through point D. Line B C extends to form exterior angle that is 135 degrees. Angle C A B is 75 degrees. What is m∠ABC? M∠ABC = 15° m∠ABC = 45° m∠ABC = 60° m∠ABC = 75°

Answer 1

45 deg

Explanation:

Answer 2

m∠ABC = 45°

Explanation:

See the attached figure.

As shown in the figure

Line C B extends through point D to form the exterior angle that is 135 degrees.

So, m∠ABD = 135°

But m∠ABC + m∠ABD = 180°

∴m∠ABC = 180° - m∠ABD = 180° - 135°= 45°

Also, we should know that

m∠ABD = m∠BAC + m∠ACB

So, m∠ACB = 135° - 75° = 60°

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Very important note:

If we replaced the location of B and C

SO, m∠ABC = 60° and m∠ACB = 45°

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