Question

triangle bcd is rotated 80° clockwise about the origin to form δklm. if m∠klm = 30°, what is m∠bcd?
a. 50°
b. 30°
c. 110°
d. 80°

Explanation:

Step1: Recall the property of rotation

Rotation is a rigid transformation. Rigid transformations (rotations, translations, reflections) preserve the shape and size of the figure. So, if \(\triangle BCD\) is rotated to form \(\triangle KLM\), then \(\triangle BCD\cong\triangle KLM\).

Step2: Use the property of congruent triangles

For congruent triangles \(\triangle BCD\) and \(\triangle KLM\), corresponding angles are equal. That is, \(\angle BCD\) and \(\angle KLM\) are corresponding angles. So, \(m\angle BCD = m\angle KLM\).

Answer:

B. \(30^{\circ}\)