Question

Angle C in triangle ABC has a measure of 17∘ . Triangle ABC is rotated 37∘ clockwise around point A to create triangle A'B'C'. Triangle A'B'C' is rotated 45∘ counter clockwise around point C' to create triangle A""B""C"". What is the measure of angle C"" in triangle A""B""C""?

Answer 1

The measure of angle C"" in triangle A""B""C"" is 81°.

Step-by-step explanation:

To find the measure of angle C"" in triangle A""B""C"", we need to consider the angles in the original triangle ABC and the rotations that have been applied. Angle C in triangle ABC has a measure of 17°. Triangle ABC is rotated 37° clockwise around point A to create triangle A'B'C', and then triangle A'B'C' is rotated 45° counter clockwise around point C' to create triangle A""B""C"".

Since the total angle sum of a triangle is always 180°, we can find the measure of angle C"" by subtracting the measures of angles C and the two rotation angles from 180°.

Let's calculate:

Measure of angle C"" = 180° - Measure of angle C - Measure of first rotation angle - Measure of second rotation angle = 180° - 17° - 37° - 45° = 81°.