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Triangle exterior angle theorem worksheets

Solve eight exact adjacent-exterior equations with one variable expression and two numeric givens. Choose single-variable, algebraic-expression or mixed practice, with matching Letter and A4 previews and answer keys.

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Match each numbered sector to its listed value. Set the adjacent exterior angle equal to the two remote interior angles, then solve for x. Diagrams are not to scale.

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Connect one exterior angle to two remote interiors

Every sheet has eight schematic triangles. One numbered sector is an adjacent exterior angle, and the other two numbered sectors are the remote interior angles. Match those sectors to Angle 1, Angle 2 and Angle 3 in the list.

Write exterior angle = remote interior + remote interior, then solve for x. Exactly one printed value contains x. The drawings are intentionally not to scale, and the answer line asks for the variable value without a degree sign.

Learning objective

What this activity builds

Use the fact that one adjacent exterior angle equals the sum of the two remote interior angles to build and solve a positive-integer linear equation.

Worked example

The exterior angle is 3x + 2 degrees. The two remote interior angles are 62 degrees and 90 degrees. What is x?

x = 50.

Use 3x + 2 = 62 + 90. Subtract 2 to get 3x = 150, then divide by 3. The requested answer is the variable value 50, not the evaluated exterior angle 152 degrees.

Teaching notes

Make the practice count

  • Locate the exterior sector first, then identify the two interior sectors that do not share its vertex.
  • Write exterior = remote interior + remote interior before substituting the printed values.
  • Treat a printed 90-degree value as a numeric given; the schematic drawing does not add an unstated right-angle fact.
  • Substitute the solved x into the expression and verify that the exterior equals the two remote interiors.

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Math SheetNameScore/ 8TeacherDateTriangle exterior angle theoremUse the exterior angle and the two remote interior angles to solve for x. Diagrams are not to scale.1.123Angle 1:x°Angle 2:161°Angle 3:89°x =2.123Angle 1:112°Angle 2:x°Angle 3:63°x =3.123Angle 1:74°Angle 2:21°Angle 3:x°x =4.123Angle 1:x°Angle 2:148°Angle 3:52°x =5.123Angle 1:109°Angle 2:x°Angle 3:50°x =6.123Angle 1:65°Angle 2:x°Angle 3:27°x =7.123Angle 1:32°Angle 2:140°Angle 3:x°x =8.123Angle 1:49°Angle 2:155°Angle 3:x°x =math-sheet.comPage 1 / 1

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