What is the m∠ADC? (I will attach picture)

Question

What is the m∠ADC?    (I will attach picture)

sarahc · Answer

attachment

anonymous · Answer

Isos triangle thm, angles D and A are congruent.
Since ext angle = sum of two remote int angles,
115 = m<A +m< D
Since they're the same,
115 = 2m<ADC
m<ADC = 115/2

sarahc · Answer

Thank you !!

anonymous · Answer

@Luis Rivera, the angles opposite the congruent sides are A and D, not A and ACD. When you said m<ADC = 180 - 130 = 50, that relied on 130 being the measure on the other two angles. That number came from 65 * 2, but angles A and ACD are not congruent. A is congruent to D, not ACD.

anonymous · Answer

On the picture you marked that A and D were congruent. If you say that m<ADC = 50, then m<A = 50 as well. Then by defn supplementary, the third angle is 65 degrees.

180° in a triangle, but 50 + 50 + 65 doesn't = 180. It = 165.