Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
If a ray splits an angle into two non-overlapping parts, the measures of the parts add up to the measure of the whole. A 90° angle split into a 35° part and an unknown part means the unknown part is 90 - 35 = 55°. Fourth graders use this additive property to find missing angles on diagrams, often writing an equation with a symbol for the unknown, such as 35 + x = 90.
Two special cases come up again and again. Angles that together form a straight line add to 180°, and angles that fill a right angle add to 90°. Angles that go all the way around a point add to 360°. Real-world problems include the turn of a door, the hands of a clock or slices of a pie chart. Students measure parts with a protractor to confirm that the sums really work, which builds confidence in the property before they rely on it for reasoning without measuring.
Students sometimes treat any angle that looks square as a right angle and subtract from 90. Check for a right angle mark or given measure before using 90.
When two angles sit on a straight line, students may not see that they sum to 180°. Measuring several examples makes the pattern clear.
If the parts overlap, their sum is more than the whole. The additive property only works when the parts do not overlap.
Three angles sit side by side on a straight line. Two measure 48° and 67°. What is the third angle, x?
Answer: The third angle measures 65°.
Use pattern blocks: the angles of several blocks fit together around a point or along a line, and students can add the known angles to check that they total 360° or 180°. Then move to drawn diagrams with labeled parts and one unknown.
Assessments usually give a diagram with one unknown and expect an equation and solution. Requiring the equation, not just the number, builds the algebraic habit that continues into middle school angle work.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 55 (also accepted: 55°, 55 degrees)
A right angle is 90°, so 35 + x = 90 and x = 90 - 35 = 55°.
Answer: 68 (also accepted: 68°, 68 degrees)
Angles on a straight line add to 180°, so the other angle is 180 - 112 = 68°.
Answer: D) 85 + x = 150
The parts add to the whole: 85 + x = 150, so x = 65°.
Answer: 125 (also accepted: 125°, 125 degrees)
Angles around a point add to 360°. 360 - 140 - 95 = 125°.
Answer: B) 65°
The turns add: 25 + 40 = 65°.
Answer: 60 (also accepted: 60°, 60 degrees)
A straight angle is 180°, and 180 ÷ 3 = 60°.
A full lesson with slides, activities and an exit ticket on additive angles and unknown angles, pitched to grade 4 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 4.MD.C.7 with an answer key, ready in about a minute.
Make a worksheet →Turn additive angles and unknown angles into a quiz students answer online that marks itself, with a class summary for you.
Build a test →It means you can add the measures of non-overlapping parts of an angle to get the measure of the whole angle, just as you can add lengths of parts of a line segment.
In seventh grade, 7.G.B.5 uses facts about supplementary, complementary, vertical and adjacent angles to write and solve equations for unknown angles.