Question

В треугольнике АВС угол А равен 66 , АД - биссектриса этого треугольника. Через точку Д проведена прямая. параллельная АС и пересекающая сторону АВ в точке М. Найдите углы треугольника АМД.

Answer 1

∠ВАД=∠А/2=33°.
Так как ДМ║АС и АД - секущая, то ∠МДА=∠ДАС=33°.
∠АМД=180°-∠МАД-∠МДА=180°-33°-33°=114°.
Ответ: углы тр-ка АМД равны 33°, 114° и 33° соответственно.

Answer 2

Given information:

- In triangle ABC, angle A = 66 degrees, and AD is the bisector of triangle ABC. - A line is drawn through point D, parallel to AC, and intersects side AB at point M.

To find:

- The angles of triangle AMD.

Solution:

Since AD is the bisector of triangle ABC, we can use the angle bisector theorem to find the ratio of the lengths of AB and BC.

According to the angle bisector theorem: AB/BC = AD/DC

Since AD is the bisector, we have: AD/DC = AB/BC

Let's assume: AB = x BC = y

Using the given information, we have: AD/DC = x/y

Since AD is parallel to AC, we can apply the corresponding angles theorem to find the angles of triangle AMD.

Angle AMD = Angle DAC (corresponding angles)

Angle DAC = Angle BAC - Angle BAD = 66 degrees - (180 degrees - Angle A) = Angle A - 114 degrees

Therefore, the angles of triangle AMD are: - Angle AMD - Angle MAD = Angle A - 114 degrees - Angle DMA = 180 degrees - (Angle A + Angle MAD)

To find the exact values of these angles, we need to know the values of angles A, MAD, and DMA.