Lesson Worksheet: Finding Unknown Angles Mathematics • 4th Grade

In this worksheet, we will practice finding the measure of unknown angles by using that angles around a point sum to 360 degrees and angles on a straight line sum to 180 degrees.


Find the missing angle in the given shape.


If ∠𝐢𝐴𝐡=50∘, find ∠𝐢𝐴𝐷.


In the given circle, if βˆ π΅π‘‚πΆ+βˆ πΆπ‘‚π·=200∘ and βˆ π΄π‘‚π·=100∘, find the measure of βˆ π΄π‘‚π΅.


In the given shape, ∠𝐷𝐸𝐹=55∘, ∠𝐡𝐸𝐹=140∘, and ∠𝐢𝐸𝐷=40∘. Find the measure of ∠𝐢𝐸𝐡.

Hint: Diagram not drawn to scale.


Sophia has 4 pieces of tile. The measure of one angle of each piece is 40∘, 54∘, 51∘, and 36∘. Which two pieces should she use side by side to make a right angle?

  • Athe 54∘ piece and the 51∘ piece
  • Bthe 40∘ piece and the 51∘ piece
  • Cthe 51∘ piece and the 36∘ piece
  • Dthe 54∘ piece and the 36∘ piece


Find the measure of the unknown angle.


Find the unknown angle.


Which of the following equations can you use to find the unknown angle?

  • A100βˆ’180=
  • B100+90=
  • C180βˆ’100=
  • D90βˆ’100=
  • E90+100=


Find the value of π‘₯ and the value of 𝑦.

  • A155, 80
  • B155, 75
  • C160, 75
  • D150, 70
  • E160, 70


Michael and Anthony live on opposite ends of Main Street. Their school is on Chestnut Street as shown on the map.

Michael rode his bike from his house to school. He turned onto Chestnut Street at an angle of 125∘.

Fill in the blank: If Anthony rides his bike from his house to school, he will turn onto Chestnut Street at an angle of .

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