Answer:
See below
Step-by-step explanation:
DOK 3
[tex] In\: \triangle ABC, \:\\
m\angle A + m\angle B + m\angle C = 180\degree \\\\
m\angle A + 76\degree + m\angle C = 180\degree \\\\
m\angle A + m\angle C = 180\degree - 76\degree \\\\
m\angle A + m\angle C = 104\degree \\\\
\frac{1}{2} (m\angle A + m\angle C) =\frac{1}{2}\times 104\degree \\\\
\red{\bold{\frac{1}{2} (m\angle A + m\angle C) = 52\degree}}... (1)\\[/tex]
Since, AD and DC are bisectors of [tex] \angle A \: \&\: \angle C[/tex] respectively.
[tex] m\angle DAC= \frac{1}{2}m\angle A... (2)\\\\
m\angle DCA= \frac{1}{2}m\angle C...(3) \\[/tex]
Adding equations (2) & (3), we find:
[tex] m\angle DAC+m\angle DCA= \frac{1}{2}(m\angle A+m\angle C).... (4)\\[/tex]
From equations (1) & (4)
[tex] m\angle DAC+m\angle DCA= 52\degree... (5)\\\\
In \triangle ADC, \\
m\angle ADC + m\angle DAC +m\angle DCA = 180\degree... (6)\\\\[/tex]
From equations (5) & (6), we find:
[tex] m\angle ADC + 104\degree = 180\degree... (6)\\\\
m\angle ADC = 180\degree - 52\degree \\\\
\huge\purple {\boxed{m\angle ADC = 128\degree}}
[/tex]
DOK 4:
Let the measures of the angels 1, 2 and 3 be 4x, 5x and 6x respectively.
Therefore,
4x + 5x + 6x = 180°
15x = 180°
x = 180°/15
x = 12°
4x = 4*12° = 48°
5x = 5*12° = 60°
6x = 6*12° = 72°
[tex] m\angle 1 = 48\degree \\\\
m\angle 2 = 60\degree \\\\
m\angle 3 = 72\degree \\[/tex]
