Question

ABCDE is a regular pentagon. The bisector of angle A of the pentagon meets the side CD in point M. Show that ∠AMC = 90⁰.

Answer 1

inal answer:

To show that ∠AMC = 90⁰, we can prove that the triangle AMC is a right triangle by using the symmetry of a regular pentagon.

Step-by-step explanation:

To show that ∠AMC = 90⁰, we can prove that the triangle AMC is a right triangle. Since ABCDE is a regular pentagon, all angles are equal, so ∠ABC = ∠ADC.

Since the bisector of ∠A meets side CD at point M, we know that ∠AMC = ∠ABC/2.

Therefore, ∠AMC = ∠ADC/2.

Since ∠ADC and ∠ABC are equal based on the symmetry of a regular pentagon, we can conclude that ∠AMC = ∠ABC/2 = ∠ADC/2 = 90⁰. Thus, ∠AMC is a right angle.