Answer:
The measure of ∠BCD would be 30°. i.e. m∠BCD = 30°.
Step-by-step explanation:
As triangle BCD is rotated 80° clockwise about the origin to form ΔKLM. We have been given m∠KLM = 30°.
We have to find m∠BCD?
As it is clear that when we rotate, reflect or translate any figure, we just make the image of original object. So, ΔKLM could be termed as the image of ΔBCD when a triangle BCD is rotated 80° clockwise about the origin to form ΔKLM.
As reflection, rotation and translation can be termed as rigid transformation, meaning the shape and size of the image and original object remains the same. In other words, we can establish the fact that image and original object (preimage) are congruent to each other.
As ΔKLM can be termed as a rigid transformation of ΔBCD, Hence they will be congruent to each other.
So,
ΔKLM ≅ ΔBCD
As we know that corresponding parts of congruent triangles are termed as congruent - according to CPCTC.
So,
∠BCD ≅ ∠KLM
As the measure of m∠KLM = 30°, and ∠BCD ≅ ∠KLM.
So, the measure of ∠BCD would be also 30°. i.e. m∠BCD = 30°.
Keywords: rotation, reflection, translation, triangle
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