West Virginia Grade 4 Math

The smaller angle is part of the whole

Angle ABC measures 110°. Ray BD lies inside it and divides it into two non-overlapping angles: ABD measures 35°, and DBC is unknown. Find the measure of DBC. A student adds 110° and 35°. Explain why that calculation does not give the missing part.

Follow the reasoning

The two non-overlapping parts together make the 110° whole, so 35° + x = 110°. Subtracting 35° gives x = 75°, and the check is 35° + 75° = 110°. The student adds the whole angle to one part already contained in it, producing 145° instead of finding the remaining part. The information about BD being inside ABC matters: it establishes which adjacent parts make the supplied whole. An unknown angle need not be guessed from a picture when its measure can be calculated from the stated relationship.

Check the explanation

This task supplies angle measures and an interior ray; it does not ask for a protractor reading from a screen. The vertex is B in all three angle names. A sum of angle measures represents the stated whole only when the parts fill it without overlap.

Try the next step

Change the whole to 125° and the known part to 40°. Write 40° + x = 125°, find x = 85°, and check the sum. Explain why making the whole larger does not automatically make both parts larger.

West Virginia reference for this worked activity

The West Virginia mathematics policy and standards page provides grade-specific documents under Policy 2520.2B. The linked Grade 4 document includes Mathematical Habits of Mind and content standards. These should be developed together in classroom work. Read the complete requirements and the school’s current curriculum sequence. The reference below selects one worked focus.

This selected reference identifies the activity focus. The complete standard and grade curriculum include additional work. These labels do not certify alignment of every independent lesson, worksheet, or quiz in the broader directory.

Choose a next task from the student’s explanation

Use a different set of numbers to check whether the student can explain the same relationship. If the explanation is unclear, return to the model; if the reasoning is sound but a calculation is wrong, work through a shorter calculation and check it against the model. Use the related learning resources alongside the teacher’s assigned goals.

The West Virginia Department of Education General Summative Assessment overview lists English language arts and mathematics in Grades 3–8, with science in Grades 5 and 8. Grade 4 is included in that mathematics range. Follow the school’s current directions and accommodations. Independently published practice follows its own timing, tools, question count, and scoring; its result does not establish a state performance level. This original activity is not an official state assessment question. Read West Virginia assessment guidance.

State sources and the selected complete PDF page checked October 6, 2026. Confirm later guidance and local assignments before planning assessment preparation.