Question

Angle ABC is formed by segments AB and BC on the coordinate grid below: A coordinate plane is shown. Angle ABC has vertices at 3 comma 4 and 5 comma 3 and 3 comma 2 and measures 53.13 degrees. Angle ABC is rotated 90 degrees counterclockwise about the origin to form angle A′B′C′. Which statement shows the measure of angle A′B′C′? m∠A′B′C′ = 90 degrees m∠A′B′C′ = 180 degrees m∠A′B′C′ = m∠ABC m∠A′B′C′ = 2 × m∠ABC

Answer 1

Answer:

m∠ABC = m∠A'B'C'

Step-by-step explanation:

We are given a ΔABC with the co-ordinates ( 3,4 ), ( 5,3 ) and ( 3,2 ) along with ∠ABC = 53.13°

Now, it is given that ΔABC is rotated counter-clockwise by 90° to make the  ΔA'B'C'.

So, we get a new triangle having co-ordinates ( -4,3 ), ( -3,5 ) and ( -2,3 ).

Since, rotation is a transformation that does not change the side length or the angle measure i.e. it preserves the congruence.

So, we get that ∠A'B'C' = 53.13°

Hence, ∠ABC = ∠A'B'C' = 53.13° i.e. m∠ABC = m∠A'B'C'