Find Unknown Angles Using Addition and Subtraction

Students solve for unknown angle measures in diagrams by writing and solving addition or subtraction equations. Problems include finding a missing angle when a larger angle is decomposed into two parts, using straight angles (180°) and right angles (90°) as known references.

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Grade 4 · Angle Addition and Unknown Angles · question 1 of 3

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20 rungs. A star at the top.

Find the missing part of angle SOU.

Your answer:

How it is taught

0:00 of 3:40

A straight angle measures 180.

If you know one part, subtract to find the rest.

Read it: Parts add up to the whole

Angle ABC is 45° and angle CBD is 70°. They sit side by side with no overlap, so angle ABD is 45° + 70° = 115°.

Find the parts that sit side by side, with no overlap.
To find the whole, add the parts: 45 + 70 = 115.
To find a missing part, take the known part from the whole: 115 − 45 = 70.

The parts fill the whole angle exactly, so their measures add up to it.

A missing part is what is left of the whole after the known part.

A straight line makes a straight angle: 180°, so 2 parts of a straight angle add up to 180°.

Parts that do not overlap add up to the whole angle.

Adding the whole and a part: 115 + 45 = 160.

The whole is already the biggest. Take the part away: 115 − 45 = 70.

A straight angle is split into 2 parts. One part is 30°. How many degrees is the other part? — 150. A straight angle is 180°, so the other part is 180 − 30 = 150.

35° + ? = 90°

When a big angle is split into smaller pieces, we can find a missing piece using addition and subtraction.

Here's a right angle. The little square in the corner tells us it measures exactly ninety degrees.

Grade 4 · Splitting a right angle into two parts

Now a new ray cuts the right angle into two smaller angles.

One of the smaller angles measures thirty-five degrees.

The other one is a mystery. Let's call it question mark until we find it.

The two pieces have to add up to the whole. So thirty-five plus our unknown equals ninety.

To find the unknown, we flip it around. Question mark equals ninety minus thirty-five.

Ninety minus thirty-five is fifty-five.

The missing angle is fifty-five degrees. Nice work!

Now you try. Find the missing part of this angle. What is the missing part?

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

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MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

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