Question

If m∠ATB = 20°, m∠BTD = 72°, and m∠CTD = 38°, what is m∠ATC?

Answer 1

Answer: m∠ATC = 54°

Explanation:

Ok, we know that:

m∠ATB = 20° and m∠BTD = 72°

then we must have that the angle between A and D, is equal to the sum of the angles between A and B, and B and D, or:

m∠ATD = m∠ATB + m∠BTD = 20° + 72° = 92°

Now, we also know that m∠CTD = 38°

And the angle:

m∠ATC will be equal to the angle between A and D, minus the angle between C and D, or:

m∠ATC = m∠ATD - m∠CTD = 92° - 38° = 54°