Recognise angle measure as additive; find unknown angles by adding or subtracting on a diagram using equations with a symbol for the unknown
Angles on a straight line add to 180 degrees when they sit side by side and exactly fill the straight angle with no gaps or overlaps. Angles around a point add to 360 degrees when they fill one full turn with no gaps or overlaps. A given whole angle may measure 90, 115, 130, 150 or 200 degrees. To find a missing part, add the known parts, then subtract from the given whole.
Angle measure adds up. When an angle is split into parts that exactly fill it with no gaps or overlaps, the parts add together to make the whole angle. To find a missing part, subtract the known part from the whole. Watch which total you use. If the whole angle is given, that number is the total, whether it is 90, 115, 130, 150, 200 or any other value.
Two angles sit side by side on a straight line, exactly filling it. One angle is 40°, and the other is x°. Write 40 + x = 180. Subtract 40 from both sides: x = 140°. Check: 40 + 140 = 180.
Three angles meet at a point and fill one full turn with no gaps or overlaps. Two are 130° and 140°, and the third is x°. Write 130 + 140 + x = 360. That is 270 + x = 360, so x = 90°. Check: 130 + 140 + 90 = 360.
To find a missing angle, first find the total: 180° for a straight angle, 360° for angles filling one full turn, or the given whole angle. Then subtract the angles you already know. What is left is your missing angle. Check by adding all the parts back together. For example, if you found x = 140 from 40 + x = 180, check: 40 + 140 = 180.
Give the unknown angle a letter, write an equation using the total, solve for it, then check by adding the parts back.
Six fresh original tasks (x1-x6) and one fresh original reading (reading3) authored for this topic. Two Khan Academy articles retained and adapted: Finding missing angles in right angles and straight lines (academy:article:4th-grade-math-eureka-squared-aligned:x5ec47d8527d3c5b0) and Finding missing angles around a point (academy:article:4th-grade-math-eureka-squared-aligned:xb18687f13f63ec41). Two Khan Academy videos retained: Finding an unknown angle measure (academy:video:4th-grade-math-eureka-squared-aligned:x36b65adcaebd92e0) and Decomposing an angle (academy:video:4th-grade-illustrative-mathematics:x6c2451f9). Two Khan Academy videos newly selected: Measuring angles in degrees (academy:video:4th-engage-ny:263439060) and Recognizing angles (academy:video:4th-engage-ny:x1781a3d6). All corpus licenses are null and unverified.
A drawbridge tilts up from a flat road. The road rays extend in opposite directions from the hinge, forming a straight angle of 180° above the road. The raised bridge ray splits that straight angle into two parts that exactly fill it with no gaps or overlaps. Give the missing angle a letter, x.
The bridge tilts 65° from the flat road. The angle above it is x°. Which equation matches?
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