Question

Practice constructing triangles with given dimensions.

Construct a triangle with the given dimensions:

angle measure of 39°

angle measure of 76°

angle measure of 65°

You can create
with the given measurements.

Answer 1

Yes — those three angles sum to 180° (39 + 76 + 65 = 180), so a triangle with those interior angles exists (unique up to scale). Here are simple ways to construct one.

Method A — using a protractor (quick)
1. Draw a base segment AB of any convenient length (for example 6 cm).
2. At A use the protractor to draw a ray making a 39° angle with AB (inside the half‑plane you want the triangle to lie in).
3. At B use the protractor to draw a ray making a 76° angle with BA (again inside the same half‑plane).
4. Let the two rays intersect at C. Connect C to A and B. Triangle ABC has angles 39°, 76°, 65°.

Method B — straightedge + compass (same idea; use protractorless methods to transfer angles)
1. Choose base AB (any length).
2. Construct at A an angle of 39° (use angle‑transfer constructions or repeated angle bisectors if you need pure compass/straightedge).
3. Construct at B an angle of 76° on the same side of AB.
4. The intersection of those two rays is C; connect A–C and B–C.

Optional numeric example (base AB = 6 cm)
- Place A at (0,0) and B at (6,0).
- Ray from A at 39°: y = tan(39°) x.
- Ray from B at absolute angle 104° (because the internal angle at B is 76° measured from BA): y = tan(104°)(x − 6).
- Solving gives C ≈ (4.995, 4.045). Distances: AC ≈ 6.427 cm, BC ≈ 4.168 cm. Angles are 39°, 76°, 65° (within rounding).

Note: Only the angles are fixed; the triangle’s size is arbitrary (all such triangles are similar).