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## 7th grade foundations (Eureka Math/EngageNY)

### Unit 6: Lesson 2

Topic B: Foundations

# Angle types review

Review the following types of angles: acute, right, obtuse, and straight.  Identify and draw types of angles in some practice problems.

### Summary of angle sizes

Angle typeAngle size (in degrees)
AcuteBetween 0, degrees and 90, degrees
RightExactly 90, degrees
ObtuseBetween 90, degrees and 180, degrees
StraightExactly 180, degrees

### Right angles

A right angle is a 90, degrees angle. A right angle is in the shape of a perfect corner, like the corner of a rectangular sheet of paper. Below is an example of a right angle.
One ray extends to the right of the vertex. Another ray extends upward. A square at the vertex connects the rays to represent a perfect corner, or a right angle.

### Straight angles

A straight angle is a 180, degrees angle. A straight angle looks like a straight line. Below is an example of a straight angle.
A straight line with a half circle on top and at the center of the line to represent a straight angle.

### Acute angles

An acute angle is an angle whose degree measure is less than 90, degrees. Below is an example of an acute angle.
A ray extends to the right of the vertex. Another ray extends to the right and upwards from the vertex. A curved line connects the rays to represent an angle, in this case an acute angle, which has a degree measure less than 90 degrees.
When we compare an acute angle to a start color #11accd, start text, r, i, g, h, t, space, a, n, g, l, e, end text, end color #11accd, we can see that an acute angle is less than 90, degrees.
The acute angle from above set inside a 90 degree angle, called a right angle. Comparing the angles, the acute angle has a smaller degree of measure than the right angle.

### Obtuse angles

An obtuse angle is an angle whose degree measure is greater than 90, degrees but less than 180, degrees. Below is an example of an obtuse angle.
A ray extends to the right of the vertex. Another ray extends up and to the left of the vertex. A curved line connects the rays to represent an angle, in this case an obtuse angle, which has a degree measure of greater than 90 degrees but less than 180 degrees.
When we compare an obtuse angle to a start color #11accd, start text, r, i, g, h, t, space, a, n, g, l, e, end text, end color #11accd, we can see that an obtuse angle is greater than 90, degrees.
The obtuse angle from above with a 90 degree angle, called right angle, set inside it. Comparing the angles, the obtuse angle has a greater degree of measure than the right angle.
When we compare an obtuse angle to a start color #1fab54, start text, s, t, r, a, i, g, h, t, space, a, n, g, l, e, end text, end color #1fab54, we can see that an obtuse angle is less than 180, degrees.
The obtuse angle from above set on a straight angle, or straight line. Comparing the angles, the obtuse angle has a smaller degree of measure than the straight angle.

### Practice set 1: Identify angles

Problem 1A
Is the following angle acute, right, obtuse, or straight?
A ray extends from the vertex towards between 3 and 4 o'clock. A second ray extends from the vertex towards 5 o'clock. An arc connects these two rays.

Want to try more problems like this? Check out this exercise.

### Practice set 2: Angles in diagrams and images

Problem 2A
What type of angle is the angle highlighted in green below?
The letter K. Inside the top angle of the letter K, a ray extends from the vertex towards 12 o'clock. A second ray extends from the vertex towards between 1 and 2 o'clock. An arc connects these two rays.

Want to try more problems like this? Check out this exercise.

### Practice set 3: Drawing angle types

Problem 3A
Drag the vertex of the angle to place the vertex at point start text, A, end text.
Drag another point on the angle to make one of the rays go through point start text, B, end text.
Make the other ray go through one of the unlabeled black points to create a straight angle.
The arc symbol near the vertex indicates the angle being measured.

Want to try more problems like this? Check out this exercise.

## Want to join the conversation?

• is there any angle that could be greater than 180 degrees?
• no. After 180 degrees it starts bending backwards, and it would be a acute angle again. A circle equals 360 degrees though.
• How is this "Right". Saying that everything around me is ATLEAST Right, Obtuse or strait? How and why? And if you go on drawing right, acute and obtuse angles then they don't let you make one how ever you want on the dots?
• Is there an angle over 720 degrees?
• Yes, angles can have any angle measure. But since there's only 360 degrees in a circle, we usually don't write angles any bigger than 360. A 720 degree angle is the same as a 360 degree angle.
• the last one confused me a little bit
• Yeah it was very confusing
• 9+9 =18 but you add a zero
to 18 90+90 = 180
• so true and right DeAndre.
• Is a straight angle a 180 degree angle
• yes because 180 degree angle is straight like a straight angle
• hi am a new person for khan academy