Problem
Point C sits on straight line BD, so 110° and angle ACD together make a straight 180°, giving ACD = 70°.
The base is a flat 180-degree line split into the two angles at C.
4.MD.C.7Identify SubproblemsTriangle ACD's three angles (60°, ACD = 70°, and a) sum to 180°, so a = 180 − 60 − 70 = 50°.
Every triangle's three corners always total 180 degrees, so the third corner is the leftover.
4.MD.C.7Identify SubproblemsIn triangle ACD, angle a equals 180 degrees minus the 60-degree angle at A minus the 70-degree angle at C.
The three corners of triangle ACD - the 60 at A, the angle at C, and a at D - fill exactly 180 degrees all together.
Every flat triangle's three corners always add up to the same 180 degrees.
The corner at C measures 70 degrees, the part of the flat base left over once the 110-degree angle is taken out.
Angles ACB and ACD sit side by side on the straight base BD, so the two of them fill 180 degrees.
The 180-degree base is one whole split with no gap into the 110-degree angle and the angle at C, so those two parts add back to it.
Taking the known 110-degree part away from the 180-degree whole is subtraction undoing the adding, which hands back the other part.
Because the three angles must total 180 degrees, angle a is simply what stays after the 60 and the 70 are removed.
The 180 degrees is one whole, and the three angles are its parts with no gap or overlap, so they add back to it.
Subtraction undoes the adding, so pulling the two known angles out of 180 leaves the missing angle a by itself.
Split the base with the 180-degree line, then the triangle's 180-degree rule hands you angle a - pure Grade 4 angle adding!