Problem
Through C, draw a horizontal line parallel to AB and DE. It splits the angle at C into a left part and a right part.
Sliding a parallel line through the corner lets each side of the bend talk to a line it is parallel to, turning one hard angle into two friendly ones.
4.G.A.1Draw A DiagramBC crosses AB and the auxiliary line, so the left part at C is the same-side partner of the 120 deg at B: 180 deg - 120 deg.
Between two parallel lines, the two same-side angles add to a straight 180 deg, so the partner of 120 deg is 60 deg.
4.MD.C.7Identify SubproblemsWhere segment BC crosses parallel line AB and the auxiliary line through C, the left part of the bend at C measures 180 degrees minus the 120 degree angle at B, which is 60 degrees.
The 120 degree angle at B and the left part of the angle at C are same-side interior angles made where BC cuts the two parallel lines, and a same-side pair always fills a straight 180 degrees together, so the left part is what is left after taking 120 from 180.
Line BC cuts across both parallel lines, and a line crossing two parallels makes the matching corner angles equal, so the angle BC opens at C in that matching corner is the same 120 degrees it opens at B.
That matching 120 degree angle at C and the left part of the bend sit side by side along the straight auxiliary line through C, so the two of them together make one straight angle.
CD crosses the auxiliary line and DE. The interior angle at D is 110 deg, so the co-interior angle (right part at C) is 180 deg - 110 deg.
Same idea on the right: the same-side partner of 110 deg is 70 deg.
4.MD.C.7Identify SubproblemsThe angle at C is the sum of its left and right parts.
Angle measures simply add when two angles sit side by side around the same vertex.
4.MD.C.7Identify SubproblemsSlide a parallel line through the bend and the tricky angle splits into two easy 'straight-line leftovers' you just add up!