I’m pretty sure you’re acquainted with a protractor. If not, a protractor is usually provided to measure up an edge accurately.

You are watching: How to measure angles without a protractor

What if there’s no protractor in hand? concern no much more because you deserve to measure an angle even with no protractor.

Here’s how:

Step 1: acquire a ruler and also measure the precise distance of both political parties from the origin point of the angle (Should it is in the similar distance for both sides). Take it a pen and document to record all the measurements.

Step 2: Label the distance as “D” and mark the two points top top the angle. It should be a length away native the allude of origin. Labeling after ~ you measure up it will help you identify each angle suggest easily.

Step 3: Use the ruler again to find the accurate distance between the 2 points top top the angle and record the dimensions on the paper.

Step 4: You will should label the measure distance in between the 2 points together “E.” This is to identify it native the previous measurement you did. Fail to document will result in confusion while act measurements and calculations later on on.

Step 5: Apply this Sine Formula: Angle measure = 2 x arcsin (0.5 x e/d). Input the values you’ve measured formerly for “D” and also “E.”

Step 6: Furthermore, this formula is acquired from the really equation for the provided sine steps of the side of the ideal triangle. The angle’s sine should be equal to the measure up of the opposite next of the angle and also divided through the measurement of the triangle’s hypotenuse.

Step 7: Solve the angle measure utilizing your graphing calculator. Encode number “2” and press the multiplication symbol. Then press “arcsin” and the value that is fifty percent of “D” and “E.”

Step 8: Double-check the encoded values, then press “Enter” or the “=” authorize to get the last answer or solution. Make certain you’ve encoded the right values correctly, or friend will get the dorn answer.

Step 9: For this formula, you can also use the calculator’s second an essential to fix it. Just press “arcsin,” which you deserve to see from the same crucial as the sin.

Step 10: you should get the last answer correctly as shortly as you reach this step. If you have actually a protractor or plans come grab one, later on on, you have the right to verify your answer and also check if they were specific or not.

You can additionally bisect angle without a protactor

There’s a lot that you deserve to do various other than measuring without a protractor. Talking back going back to basics, you can additionally bisect angles without making use of a protractor. For a rapid refresher, bisecting an angle means to division the angle right into two equal parts. That’s the line the you watch that splits one angle right into two same parts.

Here’s just how to bisect the angles without a protractor:

Step 1: Use a compass to and place it on the peak of the angle, i m sorry is suggest B.

Step 2: You will require to attract an arc from across each eight of the angle.

Step 3: Position her compass top top the point where it intersects an arm and draw another arc top top the within of the angle.

Step 4: Repeat the same process for the other arm without transforming the compass’ broad so the the two arms will intersect from each other.Step 5: By using a ruler, connect the vertex to the suggest where the arcs intersect, which is at point D. The bisector of abc is DB.

Step 6: To bisect the angles, use your compass and ruler because that accuracy.

Constructing one-of-a-kind Angles without a Protractor

Step 1: You will require to draw a line segment of points L and also M.

Step 2: Draw an arc throughout LM that goes up over point L.

Step 3: Move the compass to the direction whereby the point of the arc intersects point LM. Make certain you walk not readjust the broad of the compass.

Step 4: Draw one more arc that crosses the first arc the you drew.

Step 5: Then connect allude L come the suggest where the 2 arcs meet.

Important points to remember

Ensure that you make dimensions accurately. It’s always recommended come conduct measurements at the very least twice come verify the correctness.It won’t hurt come compare your answers when using a protractor. This will assist you practice and learn better.

See more: What Is The Cube Root Of 64 (Value And Simplification), What Is The Cube Root Of 64

There you have actually it! It might be simpler to measure, bisect, and also construct angles making use of protractors. However, it’s also great to note that you have the right to actually carry out it without it. Her geometry skills will additionally improve once you start doing the manually. So the following time you don’t have actually a protractor, you’re great to go!

Can you usage a ruler rather of a protractor?


A protractor
is the usual tool for the job. Once a protractor is no available, however, an plain ruler and also a calculator will certainly suffice. Host one that the present so that it is level with the ground.