A right triangle has one angle that measures 60°. what is the measure of the other acute angle?

60 degree angle is an acute angle, as angles smaller than a right angle (less than 90°) are called acute angles. In the case of a geometric angle, the arc is centered at the vertex and constrained by the sides. In the case of rotation, the arc is centered in the center of rotation and is limited to any other point and its image when rotated. Let us learn more about 60-degree angles, ways of constructing them, and solve a few examples to understand the concept better.

What is 60 Degree Angle?

60 degree angle is an acute angle in geometry and is expressed as π/3 in radians. Each angle in an equilateral triangle is equal to 60 degrees. We can construct a 60 degree angle using a compass, protractor, and a ruler and observe this angle in our daily lives in various objects.

Meaning of 60 Degree Angle

We know that an angle is formed when two rays meet at a vertex. If the angle formed at the vertex O measures 60 degrees, we call it a 60-degree angle. The measure of each angle of an equilateral triangle is 60°. Therefore, it is also called a 60-degree angle triangle. Angles can also be represented in radians i.e. pi (π) and pi (π) radians = 180°. Therefore, 60° can be expressed in radians as π/3 radians.

Constructing a 60 Degree Angle

Constructing a 60-degree angle is one of the most basic constructions, as it forms as a constructing angle for other measurements as well. Let us explore how to construct a 60-degree angle with the help of a protractor. Follow the given steps:

• Step 1: Draw a line segment OA
• Step 2: Place the protractor at the point O
• Step 3: In the outer circle of the protractor, look for 60 degrees reading, and with a pencil, mark a dot and name it C
• Step 4: Join O and C. Now, ∠AOC=60°

60 Degree Angles in Real Life

Angles are all around us. For example, when we open our mouths, our lips form an angle. When the minute hand of a clock is at 12 and the hour hand is at 2, the angle formed between the two hands is 60°. Some road signs are in the shape of an equilateral triangle, and the measure of each angle of an equilateral triangle is 60°. A 60-degree angle is used in architecture to construct designer houses, doors, and window grills.

The image below shows various examples of angles in our surroundings. Observe where you can see 60-degree angles in your surrounding areas.

Important Notes on 60 degree angle

• A 60 degree angle is an acute angle in geometry.
• An equilateral triangle is called a 60 degree angle triangle as the measure of each angle in it is equal to 60 degrees.
• We can construct a 60 degree angle using a protractor, compass, and ruler.

Related Articles

• 30 Degree Angle
• Straight Angle
• 180 Degree Angle
• Triangles

1. Example 1: In the ΔABC, use a protractor to measure ∠CAB.

   Solution: Place the protractor baseline along line AB and the center of the protractor at vertex A. Observe the reading in the protractor, which overlaps with line AC.

   

   Answer: Therefore, ∠CAB = 60°

2. Example 2: Help Josie construct an angle of 60°.

   Solution: Here are the steps that Josie can follow to construct a 60° angle

   Step-1: Draw a line OP.

   

   Step-2:

   • Place the protractor on the line OP.
   • Place the midpoint of the protractor at point O.
   

   Step-3:

   • On OP from the right, start counting from 0° in ascending order mark a point Q using a sharp pencil at the point showing 60°.
   • Remove the protractor and join OQ.
   • We get the required angle ∠QOP = 60°.
   

   Answer: Therefore, ∠QOP = 60°

Show Solution >

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FAQs on 60 Degree Angle

A 60 degrees angle is an acute angle because it is less than 90 degrees. 60° in radians is π/3 and the measure of each angle of an equilateral triangle is 60°. Therefore, it is also called a 60-degree angle triangle.

How do you Construct a 60 Degree Angle Using a Protractor?

To construct a 60-degree angle, it takes 2 arcs to draw an angle of 60. Here are the steps to construct a 60-degree angle:

Step 1: Draw a line segment PQ Step 2: Place the protractor at the point P Step 3: In the outer circle of the protractor, look for 60° reading, and with a pencil, mark a dot and name it R

Step 4: Join P and R. Now, ∠QPR=60°

What do You Call a 60-Degree Angle?

An angle whose measure is more than 0° but less than 90° is called an acute angle. Angles measuring 30°, 40°, 60° are all acute angles. Therefore a 60-degree angle is known as an acute angle.

How do You Find a 60 Degree Angle Without a Protractor?

Here are the steps required in constructing a 60-degree angle without a protractor:

Step 1: Draw a line segment (AB). With the compass on point A, draw an arc across AB and up over the above point A.

Step 2: Without changing the compass width, move the compass to the point where the arc crosses AB, and draw an arc that crosses the first one.

Step 3: Join the point A to the point where the two arcs meet (point C). ∠CAB = 60°

How Many 60 Degrees Angles Does it Take to Make a Full Turn?

Angles are measured in degrees and there are 360 degrees in one full rotation that completes one full circle. Since 60 × 6 = 360, therefore there are six 60° angles in a full turn.

What is a 60 Degree Angle in Radians?

We can express the 60 degree angle in radians using the formula: Angle in radians = Angle in Degrees × π/180. So, we have 60 degrees in radians = 60 × π/180 = π/3 radians.

The measure of 3 angles in a triangle are in a 1:2:3 ratio. What is the measure of the middle angle?

Possible Answers:

Correct answer: 60

Explanation:

The angles in a triangle sum to 180 degrees. This makes the middle angle 60 degrees.

A 17 ft ladder is propped against a 15 ft wall. What is the degree measurement between the ladder and the ground?

Possible Answers:

Correct answer:

Explanation:

Since all the answer choices are in trigonometric form, we know we must not necessarily solve for the exact value (although we can do that and calculate each choice to see if it matches). The first step is to determine the length of the ground between the bottom of the ladder and the wall via the Pythagorean Theorem: "x2 + 152 = 172"; x = 8. Using trigonometric definitions, we know that "opposite/adjecent = tan(theta)"; since we have both values of the sides (opp = 15 and adj = 8), we can plug into the tangential form tan(theta) = 15/8. However, since we are solving for theta, we must take the inverse tangent of the left side, "tan-1". Thus, our final answer is

What is the sine of the angle between the base and the hypotenuse of a right triangle with a base of 4 and a height of 3?

Possible Answers:

Correct answer:

Explanation:

By rule, this is a 3-4-5 right triangle. Sine = (the opposite leg)/(the hypotenuse). This gives us 3/5.

In a right triangle ABC, the measure of angle C is greater than 60 degrees. Which of the following statements could describe the measures of angles A and B?

Possible Answers:

Correct answer:

Explanation:

Given that it is a right triangle, either angle A or B has to be 90 degrees. The other angle then must be less than 30 degrees, given that C is greater than 60 because there are 180 degrees in a triangle.

Example:

If angle C is 61 degrees and angle A is 90 degrees, then angle B must be 29 degrees in order for the angle measures to sum to 180 degrees.

Right triangle 

Possible Answers:

Correct answer:

Explanation:

Solving this problem quickly requires that we recognize how to break apart our ratio.

The Triangle Angle Sum Theorem states that the sum of all interior angles in a triangle is 

Since this is true, we can assume that 

Thus, 

To find the value of one angle of the ratio, simply assign fractional value to the sum of the ratios and multiply by 

Thus, the shortest angle (the one represented by 

Right triangle 

Possible Answers:

Correct answer:

Explanation:

The Triangle Angle Sum Theorem states that the sum of all interior angles in a triangle must be 

The rest is simple subtraction:

Thus, our missing angle is 

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