Angle E Has What Measurement According to the Protractor?

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The easiest way to measure an angle is to use a protractor. Nonetheless, if y'all don't have a protractor handy, y'all can determine the size of an angle using the basic geometric principles of triangles. Yous'll need a scientific calculator to solve the equations. Almost smartphones are equipped with them, just you can also download a free app or access a free estimator online. The calculations yous demand to make depend on whether you lot're measuring an acute (less than 90 degrees), obtuse (more than than 90 degrees but less than 180), or reflex angle (more than 180 degrees but less than 360).^[1]

1. ane

   Depict a vertical line connecting the ii rays of the angle. To determine the number of degrees in an astute angle, connect the 2 rays to form a triangle. Line up the curt cease of your ruler with the bottom ray, then draw a vertical line intersecting the other ray using the long side of your ruler.^[2]

   • The vertical line creates a right triangle. The angle formed past the adjacent side (the bottom ray of the bending) of the triangle and the opposite side (the vertical line) measures ninety degrees.

2. 2

   Measure the length of the side by side side to find the run. Place the finish of your ruler at the vertex of the angle. Measure the length of the adjacent side from the vertex to the point where it intersects with the opposite side.^[iii]

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

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3. 3

   Measure out the length of the reverse side to find the rise. Gear up the short end of your ruler flush confronting the adjacent side of the triangle. Mensurate the length of the vertical line from the bespeak where information technology meets the adjacent side to the bespeak where it meets the upper ray of the angle (the hypotenuse of your triangle).^[4]

   • This amount is the rise value in your slope equation. If you measured five, you lot would make full in your equation so that "slope = five/vii."

4. 4

   Divide rise by 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 lot can calculate the degrees of your astute angle.^[5]

   • To go on the case, the equation "gradient = v/vii" would yield "slope = 0.71428571."

   Tip: Don't round the number earlier calculating the degrees in the angle – it could decrease the accuracy of the result.

5. 5

   Use your calculator to determine the degrees of the bending. Type the value for slope into your scientific computer, then press the inverse tan button (tan^-one). This volition give you lot the degrees of the angle.^[six]

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

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1. one

   Extend the lesser ray of the angle in a straight line. Marker your vertex with a dot, and so utilize the long side of your ruler to draw a directly line to the left of the vertex. The bottom ray of the bending should exist a single long line that extends below the open meridian ray of the angle.^[seven]

   • Brand sure your line is perfectly straight. If it is angled upwardly or down, information technology will ruin the accuracy of your equation.

   Tip: if y'all're working on unlined paper, you tin can line up the curt end of your ruler with the side of the paper to brand sure your line extension is straight.

2. 2

   Depict a vertical line connecting the pinnacle ray and the line. Line up the curt end of your ruler with the bottom ray at a point where the long side crosses the elevation ray. Follow the long side to draw a line straight up from the bottom ray that connects the two.^[8]

   • Finer, you have created a small right angle underneath the obtuse angle you want to measure out, turning the top ray of the obtuse bending into the hypotenuse of your right angle.

3. 3

   Measure the length of the lesser line from the vertex. Place your ruler below the bottom line, with the offset at the vertical line creating the right angle. Measure the length from that betoken of intersection to the vertex of the original bending.^[9]

   • Y'all're determining the slope for the angle of the acute triangle, which y'all tin use to calculate the degrees in the acute angle. The bottom line is the run value in the equation "slope = rise/run."

4. 4

   Measure the length of the vertical line. Line upwards the brusque end of your ruler with the bottom line of the small-scale acute triangle. Read up the ruler to the betoken where the vertical line meets the open ray of your birdbrained angle. This is the length of your vertical line.^[10]

   • The length of your vertical line is the rise value in the equation "slope = ascent/run." Once you know the values for both rise and run, y'all tin calculate the slope of the astute angle.

5. five

   Find the slope of the acute angle. Carve up the ascension value past the run value to determine the slope of the astute angle. You'll apply this value to calculate the degrees of the acute angle.^[xi]

   • For example, the equation "slope = 2/4" would yield "slope = 0.five."

6. 6

   Calculate the degrees of the acute angle. Enter your slope value in your scientific calculator, and so press the changed tan button (tan^-1). The value displayed is the number of degrees in the acute bending.^[12]

   • To continue the example, if your slope is 0.5, the acute angle is a 26.565-caste angle.

7. vii

   Subtract the degrees of the acute bending from 180. A flat line is a straight bending with 180 degrees. Since you drew a straight line, the sum of the acute angle you calculated and the obtuse angle volition be 180 degrees. Subtracting the degrees of the astute bending from 180 volition requite you the degrees of your birdbrained angle.^[13]

   • To go on the example, if you lot take an acute bending of 26.565 degrees, you have an birdbrained bending of 153.435 degrees (180 – 26.565 = 153.435).

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1. 1

   Identify the smaller astute angle associated with the reflex angle. A reflex angle has more than than 180 degrees just fewer than 360. This means that if you wait at the reflex angle, y'all'll also encounter an acute bending inside the rays of the reflex bending.^[14]

   • Past determining the degrees of the acute bending, y'all tin calculate the degrees in the reflex angle. Yous can use the basic slope equation and the changed tangent part on your scientific calculator to find the degrees in the acute angle.

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

2. 2

   Draw a vertical line connecting the rays of the acute bending. Line up the short end of your ruler with the ray of the angle that is horizontal rather than diagonal. Then draw a vertical line that meets the horizontal ray of the bending.^[fifteen]

   • 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 mensurate.

3. iii

   Measure the rise and the run of the acute angle. In the equation "slope = ascent/run," the rise is the length of the vertical line, or contrary side of your triangle. The run is the length of the horizontal line, or adjacent side of your triangle.^[16]

   • Measure the horizontal line from the vertex to the betoken where it meets the vertical line. Measure the vertical line from the signal where it meets the horizontal line to the signal where it meets the diagonal line.

4. four

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

   • For example, if your horizontal line measured 8 and your vertical line measured 4, your equation would exist "slope = 4/8." The gradient of your angle would exist 0.5.

5. 5

   Use your calculator to find the degrees of the astute angle. Type the value you got for the slope of the angle into your scientific estimator, then printing the inverse tangent button (tan^-1). The value displayed is the degrees of the smaller astute angle.^[18]

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

6. 6

   Decrease the degrees of the acute angle from 360. A circle has 360 degrees. Since a reflex angle is an angle of more 180 degrees, you relate it as a portion of a circle. The degrees of the reflex angle and the degrees of the smaller acute angle would add up to 360.^[19]

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

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Add together New Question

• Question

  What if the line is curvy?

  

  If at that place is no direct line, in that location's no angle to measure out. (An angle is defined as a figure formed by 2 "rays," which are straight line segments.)

• Question

  How practise I construct a vertical line?

  

  Utilize a protractor to describe 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 usually yield more precise angles than a protractor can.

• Question

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

  

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

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• Brand certain the trig functions of your scientific calculator are set to measure out in degrees, not radians.

• Gradient is the human relationship between rising and run. The unit you lot utilise to quantify the lengths of the 2 lines is irrelevant – merely brand sure you're using the same unit for both lines. In other words, if you measure the length of one line in centimeters, you should also measure out the other in centimeters.

Cheers for submitting a tip for review!

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Things Yous'll Need

• Scientific calculator
• Ruler

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Article Summary X

To measure an acute angle without a protractor, start by cartoon a vertical line connecting the ii rays of the angle to form a right triangle. Note that the angle formed by the adjacent side of the triangle and the opposite side measures 90 degrees. Next, measure out the length of the next side to find the run. Then, measure the length of the contrary side to find the rising. Once you have these measurements, divide rise by run to find the gradient, or the steepness, of the diagonal line. When y'all have this number, you can summate the degrees of your astute angle by typing the value for gradient into a scientific figurer. Finally, printing the inverse tan push button to get the degrees of the angle. To larn how to measure an obtuse angle without a protractor, proceed reading!

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