How To Draw An Angle Without A Protractor

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The easiest way to mensurate an angle is to use a protractor. However, if y'all don't have a protractor handy, you tin make up one's mind the size of an angle using the bones geometric principles of triangles. You'll need a scientific estimator to solve the equations. Virtually smartphones are equipped with them, simply y'all tin also download a free app or admission a free calculator online. The calculations you need to make depend on whether you lot're measuring an acute (less than 90 degrees), birdbrained (more than ninety degrees but less than 180), or reflex angle (more than than 180 degrees merely less than 360).^[i]

1. 1

   Draw a vertical line connecting the two rays of the bending. To make up one's mind the number of degrees in an acute angle, connect the 2 rays to class a triangle. Line upwardly the brusque end of your ruler with the bottom ray, then draw a vertical line intersecting the other ray using the long side of your ruler.^[ii]

   • The vertical line creates a right triangle. The angle formed by the adjacent side (the bottom ray of the angle) of the triangle and the contrary side (the vertical line) measures 90 degrees.

2. ii

   Mensurate the length of the adjacent side to find the run. Place the stop of your ruler at the vertex of the bending. Measure out the length of the next side from the vertex to the point where it intersects with the contrary side.^[3]

   • This amount is the run value in your slope equation, where slope = rise/run. If y'all measured 7, your equation at this point would exist "gradient = rise/7."

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3. iii

   Measure the length of the opposite side to observe the rise. Fix the brusque finish of your ruler flush against the side by side side of the triangle. Measure the length of the vertical line from the point where it meets the adjacent side to the point where it meets the upper ray of the angle (the hypotenuse of your triangle).^[iv]

   • This amount is the rise value in your slope equation. If you measured 5, you would fill in your equation and then that "slope = 5/7."

4. 4

   Divide rise past run to find the slope of the angle. The slope is the steepness of the diagonal line, or hypotenuse, of your triangle. Once you know this number, you can calculate the degrees of your acute angle.^[five]

   • To go on the example, the equation "slope = 5/7" would yield "gradient = 0.71428571."

   Tip: Don't circular the number before calculating the degrees in the angle – it could decrease the accurateness of the outcome.

5. 5

   Utilise your calculator to determine the degrees of the angle. Type the value for gradient into your scientific figurer, then press the changed tan button (tan^-one). This will requite you the degrees of the angle.^[6]

   • To continue the example, with a gradient of 0.71428571, the angle is 35.five degrees.

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1. 1

   Extend the lesser ray of the angle in a straight line. Marker your vertex with a dot, so apply the long side of your ruler to draw a straight line to the left of the vertex. The lesser ray of the angle should be a single long line that extends below the open pinnacle ray of the bending.^[7]

   • Make sure your line is perfectly straight. If it is angled up or down, information technology volition ruin the accuracy of your equation.

   Tip: if you lot're working on unlined paper, you can line upwardly the brusk finish of your ruler with the side of the paper to brand sure your line extension is direct.

2. 2

   Draw a vertical line connecting the top ray and the line. Line upwardly the short finish of your ruler with the bottom ray at a point where the long side crosses the top ray. Follow the long side to describe a line straight up from the bottom ray that connects the two.^[8]

   • Effectively, you lot take created a small correct angle underneath the birdbrained angle you want to measure, turning the top ray of the obtuse angle into the hypotenuse of your right angle.

3. 3

   Measure out the length of the bottom line from the vertex. Identify your ruler below the bottom line, with the showtime at the vertical line creating the right bending. Measure the length from that bespeak of intersection to the vertex of the original angle.^[9]

   • You're determining the slope for the angle of the astute triangle, which you can use to summate the degrees in the acute angle. The lesser line is the run value in the equation "slope = rise/run."

4. four

   Measure the length of the vertical line. Line up the short cease of your ruler with the bottom line of the modest acute triangle. Read up the ruler to the bespeak where the vertical line meets the open up ray of your birdbrained angle. This is the length of your vertical line.^[10]

   • The length of your vertical line is the rising value in the equation "slope = ascension/run." One time y'all know the values for both rise and run, you can summate the slope of the astute angle.

5. v

   Find the slope of the astute bending. Divide the rising value by the run value to determine the gradient of the acute angle. You'll apply this value to calculate the degrees of the acute angle.^[11]

   • For example, the equation "slope = 2/4" would yield "slope = 0.5."

6. six

   Calculate the degrees of the acute angle. Enter your gradient value in your scientific calculator, then press the inverse tan button (tan^-ane). The value displayed is the number of degrees in the acute angle.^[12]

   • To go on the example, if your slope is 0.5, the acute angle is a 26.565-degree angle.

7. 7

   Subtract the degrees of the acute angle from 180. A flat line is a directly bending with 180 degrees. Since you lot drew a straight line, the sum of the acute angle y'all calculated and the obtuse angle volition be 180 degrees. Subtracting the degrees of the acute angle from 180 will give y'all the degrees of your birdbrained angle.^[13]

   • To continue the instance, if you accept an astute angle of 26.565 degrees, you lot accept an obtuse bending of 153.435 degrees (180 – 26.565 = 153.435).

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1. one

   Place the smaller acute angle associated with the reflex angle. A reflex angle has more 180 degrees but fewer than 360. This means that if you expect at the reflex angle, you'll too come across an acute angle inside the rays of the reflex angle.^[14]

   • By determining the degrees of the astute angle, you tin can calculate the degrees in the reflex bending. Yous can apply the basic gradient equation and the inverse tangent function on your scientific estimator to notice the degrees in the astute angle.

   Tip: If you become confused because the angle is upside down, turn your paper and ignore the reflex angle until the concluding step.

2. 2

   Describe a vertical line connecting the rays of the acute angle. Line upwardly the short end of your ruler with the ray of the angle that is horizontal rather than diagonal. And then draw a vertical line that meets the horizontal ray of the angle.^[xv]

   • The horizontal line becomes the adjacent side of your triangle, and the vertical line becomes the opposite side of the acute angle you want to measure out.

3. 3

   Measure the rise and the run of the acute angle. In the equation "slope = rise/run," the rise is the length of the vertical line, or reverse side of your triangle. The run is the length of the horizontal line, or side by side side of your triangle.^[sixteen]

   • Measure the horizontal line from the vertex to the signal where information technology meets the vertical line. Measure the vertical line from the point where it meets the horizontal line to the point where it meets the diagonal line.

4. 4

   Dissever rise by run to find the slope of the acute bending. Plug the values you institute for the length of the vertical and horizontal lines into your slope equation. When you divide the length of the vertical line by the length of the horizontal line, yous'll get the slope for the angle.^[17]

   • For example, if your horizontal line measured 8 and your vertical line measured iv, your equation would exist "slope = 4/viii." The slope of your bending would be 0.five.

5. 5

   Utilise your calculator to observe the degrees of the acute angle. Type the value yous got for the slope of the angle into your scientific figurer, so press the inverse tangent button (tan^-1). The value displayed is the degrees of the smaller acute angle.^[eighteen]

   • To continue the example, if your slope is 0.5, the acute angle would measure 26.565 degrees.

6. half dozen

   Subtract the degrees of the acute angle from 360. A circle has 360 degrees. Since a reflex bending is an angle of more than 180 degrees, you relate it every bit a portion of a circle. The degrees of the reflex bending and the degrees of the smaller astute angle would add together up to 360.^[19]

   • To continue the example, if the smaller acute angle measures 26.565 degrees, the reflex angle would measure out 333.435 degrees.

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Add New Question

• Question

  What if the line is curvy?

  

  If there is no straight line, in that location'south no bending to measure. (An angle is defined as a effigy formed by two "rays," which are straight line segments.)

• Question

  How practice I construct a vertical line?

  

  Use a protractor to draw a line perpendicular to the top or bottom edge of the paper, or measuring with a ruler, draw a line parallel to the sides of the paper.

• Question

  How how accurate are the results for each method?

  

  Those methods tin can commonly yield more precise angles than a protractor tin can.

• Question

  What is the sum of all the angles in a triangle?

  

  All the interior angles of a triangle, no matter what blazon of triangle it is, add to 180 degrees.

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• Make sure the trig functions of your scientific calculator are set to measure in degrees, not radians.

• Slope is the relationship between rise and run. The unit of measurement you use to quantify the lengths of the ii lines is irrelevant – just make sure you're using the same unit for both lines. In other words, if you mensurate the length of one line in centimeters, you should as well measure the other in centimeters.

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Things You'll Need

• Scientific calculator
• Ruler

About This Article

Article Summary 10

To measure an acute angle without a protractor, showtime by drawing a vertical line connecting the 2 rays of the angle to course a correct triangle. Note that the angle formed past the adjacent side of the triangle and the reverse side measures ninety degrees. Next, measure the length of the adjacent side to notice the run. Then, measure the length of the opposite side to find the rising. Once you have these measurements, split rise by run to find the gradient, or the steepness, of the diagonal line. When you lot take this number, you can calculate the degrees of your acute angle by typing the value for slope into a scientific calculator. Finally, press the inverse tan button to get the degrees of the angle. To learn how to measure out an obtuse angle without a protractor, keep reading!

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