Problem
Along that line the three angles 90 degrees, b, and 50 degrees make up the 180-degree straight angle. Subtract the two known angles.
The flat line totals 180 degrees; the middle piece is what is left after the right angle and the 50-degree angle.
4.MD.C.7Identify SubproblemsAngle b equals 180 degrees with the 90-degree and 50-degree angles taken away.
The 90-degree angle, angle b, and the 50-degree angle sit next to each other along one straight line, so 90 + b + 50 must equal 180.
Angles lying side by side along a straight line always add up to 180 degrees.
Once 90 + b + 50 = 180, we get b by itself by taking the two known angles off the total, which leaves b = 180 - 90 - 50.
Subtracting undoes the adding, so removing the known parts from the total recovers the missing part b.
Angle a sits opposite the 50-degree angle across the crossing, and opposite angles are equal, so a is 50 degrees.
When two lines cross, the two angles facing each other are mirror-equal in size.
4.MD.C.7Draw A DiagramA flat line is 180 degrees and angles facing each other across a crossing match - that is all you need to find both a and b!