Geometry

Triangle angles

Change the shape. Follow the angles.

Predict, test and explain

Step 1 of 3

Predict

If you stretch a triangle until one angle is obtuse, what happens to its interior angle sum?

A+B+C=  ?A+B+C = \;?
ABC

Scroll the diagram sideways to see every label.

A≈38.7∘A \approx 38.7^\circB≈53.1∘B \approx 53.1^\circC≈88.2∘C \approx 88.2^\circ

InvestigateChange the triangle. What changes, and what stays the same?

Explore and compare

Choose the investigation above. Predict what will change before you move a control.

Try it in the simulation. Change one thing at a time.

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Hints, self-check and connections
Try a self-check

Fixed values, separate from the diagram controls.

A triangle has two interior angles of 35 degrees and 75 degrees. Find its third interior angle.

Hint

The three interior angles of a triangle total 180 degrees.

Reveal answer

The third interior angle is 70 degrees.

180∘−35∘−75∘=70∘180^\circ-35^\circ-75^\circ=70^\circ

Build an explanation

Hint 1

Change the triangle's shape and watch all three angles.

Hint 2

Bring the angles together to compare them with a straight angle.

Hint 3

The three interior angles of every triangle sum to 180°.

Worked example

This example uses fixed values, separate from the diagram controls.

A triangle has angles 48° and 67°. Find the third angle.

  1. Add the known angles: 48° + 67° = 115°.
  2. Subtract their total from 180°.

Answer: 65°.

Connect this idea

Watch out: Changing a triangle's shape changes its individual angles, but their total remains 180°.