Question

ΔBCD is rotated 80° clockwise about the origin to form ΔKLM. If m∠KLM=30°, what is m∠BCD?

A.) m∠BCD = 30°
B.) m∠BCD = 50°
C.) m∠BCD = 80°
D.) m∠BCD = 110°

Answer 1

The problem ask to calculate the angle BCD and choose among the following is the correct value or angle of BCD where as triangle BCD is rotated 80degree clockwise and the best answer among the following choices is letter A. angle BCd =30degree

Answer 2

The correct option is A.

Explanation:

It is given that ΔKLM is the image of ΔBCD after rotation of 80 degree clockwise about the origin.

Rotation, reflection and translation are rigid transformation. It means the size and shape of image and preimage are same or we can say that the image and preimage are congruent to each other.

Since ΔKLM is rigid transformation of ΔBCD, therefore both triangles are congruent to each other.

`\triangle KLM\cong \triangle BCD`

The corresponding parts of congruent triangles are congruent (CPCTC).

`\angle BCD\cong \angle KLM` (CPCTC)

The measure of angle KLM is 30°.

`\angle BCD\cong 30^(\crc)`

`\angle BCD=30^(\crc)`

Therefore option A is correct