Question

triangle abc is rotated 100° counterclockwise about point p to create δabc. what is m∠cab? a. 50° b. 100° c. 60° d. 70°

Explanation:

Step1: Recall the property of rotation

Rotation is a rigid transformation, which means that the shape and size of the triangle do not change. So, \(\triangle ABC\cong\triangle A'B'C'\).

Step2: Use the congruent - angle property

Since \(\triangle ABC\cong\triangle A'B'C'\), the corresponding angles are equal. That is, \(\angle CAB=\angle C'A'B'\).

Step3: Calculate \(\angle CAB\)

In \(\triangle ABC\), we know that the sum of angles in a triangle is \(180^{\circ}\). But we can also directly use the fact that \(\angle CAB = 70^{\circ}\) (by looking at the angle marked at vertex \(A\) in \(\triangle ABC\)).

Answer:

D. \(70^{\circ}\)