Question

ABCDE is a regular pentagon. The bisector of angle A meets the sides CD at M.

Find ∠AMC​

Answer 1

Step-by-step explanation:

Solution:-

Given : ABCDE is a regular pentagon.

The bisector ∠A of the pentagon me~ets the side CD at point M.

To prove : ∠AMC = 90°

Pr~oof: We know that, the measure of each interior angle of a regular pentagon is 108°.

• ∠BAM = 1/2 X 108o = 54o

Since, we know that the sum of a quadrilateral is 360°

In quadrilateral ABCM, we have

• ∠BAM + ∠ABC + ∠BCM + ∠AMC = 360°
• 54° + 108° + 108° + ∠AMC = 360°
• ∠AMC = 360° – 270°
• ∠AMC = 90°

Hope this helps you ☺️