Answer:
[tex]97^0[/tex]
Step-by-step explanation:
Given that the angles A, B, C in a Triangle form an arithmetic sequence where A=23 degrees.
The nth term of an Arithmetic sequence is given by the formula: [tex]T_n=a+(n-1)d[/tex]
Where:
a=first term
n=number of term
d=common difference
In this case,
[tex]Angle \:A, a=23^0[/tex]
[tex]Angle B, T_2=23+(2-1)d=(23+d)^0\\Angle C, T_3=23+(3-1)d=(23+2d)^0[/tex]
The sum of angles in a triangle is 180 degrees. Therefore:
∠A+∠B+∠C=180 degrees
[tex]23^0+(23+d)^0+(23+2d)^0=180\\69^0+3d=180^0\\3d=180^0-69^0\\3d=111^0\\d=37^0[/tex]
Therefore:
Angle C,
[tex](23+2d)^0=(23+2(37))^0=23+74\\C=97^0[/tex]
