Question Video: Finding the Measure of the Angle of Rotation | Nagwa Question Video: Finding the Measure of the Angle of Rotation | Nagwa

# Question Video: Finding the Measure of the Angle of Rotation Mathematics • First Year of Preparatory School

## Join Nagwa Classes

โณ๐ด๐ตโฒ๐ถโฒ is the image of โณ๐ด๐ต๐ถ by a counterclockwise rotation of ๐ฅยฐ about ๐ด. Find ๐ฅ.

01:41

### Video Transcript

Triangle ๐ด ๐ต prime ๐ถ prime is the image of triangle ๐ด๐ต๐ถ by a counterclockwise rotation of ๐ฅ degrees about ๐ด. Find ๐ฅ.

So, in this question, weโre given that thereโs a rotation. Triangle ๐ด๐ต๐ถ is rotated, and weโre told that the direction is counterclockwise, to give us triangle ๐ด ๐ต prime ๐ถ prime. The angle of rotation is ๐ฅ degrees, and we need to work out what ๐ฅ is.

The center of rotation of this rotation is at vertex ๐ด, which explains why thereโs no new image of ๐ด of ๐ด prime. In order to work out the angle of rotation between an object and its image, we can calculate the angle between any vertex and the image of that vertex. Letโs begin with vertex ๐ต. We know that itโs rotated counterclockwise to the image ๐ต prime. If we joined each vertex, ๐ต and ๐ต prime, with a line to the center of rotation, then to find the angle of rotation, we just need to find the angle between these two lines.

So, ๐ฅ, the angle of rotation, is equal to 37 degrees plus 69 degrees, which means that ๐ฅ is equal to 106. We can check our answer by finding the angle between ๐ถ and ๐ถ prime. To find the angle here, once again weโll be adding 69 degrees and 37 degrees, which gives us an answer of 106.

## Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

• Interactive Sessions
• Chat & Messaging
• Realistic Exam Questions