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# HOW DO WE CONSTRUCT AN ANGLE OF 290 DEGREES?

### 7 Answers

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• Anonymous
1 month ago

Make a 70 degree angle and have a good look at it.

• (1) On your paper, draw a horizontal straight line OA.

(2) Use a protractor, with O as the vertex, to

mark down an angle <AOB=70* in the clockwise direction; then the angle <AOB=

290* ,in the counterclockwise direction.

• A 290° angle cannot be constructed within the classical straightedge and compass rules.

Are you familiar with the ancient angle trisection construction challenge? It was never solved, but it was eventually proved that no general solution is possible. The only proof with which I am personally familiar was one in which it was proved that construction of a 20° angle is impossible. A 60° angle is quite a simple construction. Since a 20° construction is impossible, it must be impossible to trisect a 60° angle, and therefore angle trisection is not generally possible.

That result applies directly to your question. A 270° construction is simply a matter of perpendicular lines, an elementary construction. If it were possible to construct 290°, then that angle could be combined with a 270° angle to form a 20° angle. However, once again, that is not possible. Therefore, the 290° construction cannot be possible.

• 1) 290° is in the 4th quadrant (lower right quadrant below the +x axis)

2) The reference angle for 290° is 360 - 290 = 70°

3) Draw a line from the origin at an angle of 70° below the +x axis in the 4th quadrant

4) The angle from the +x axis counter clockwise around to the terminal line you just drew in step 3) measures 290°

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• 290 degrees has the same construction as 360 - 290 = 70 degrees.  If this is for a physical object, look up the tangent ratio for 70 degrees.  That's about 2.75, by the way.  So you draw a line (say) 1 foot long, and a line at right angles to that 2.75 feet long, making the 2 legs of a right triangle.  Draw the hypotenuse, and the angle adjacent to the 1-foot side will be 70 (290) degrees.

Or use a protractor, or computer drawing program, to get 70 degrees.

• With an angle ruler. You don't need to reinvent the wheel.

• WITH PAPER, PENCIL, AND A LITTLE BIT OF LUCK.

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