Question

In triangle $ABC$, the angles $\angle A$, $\angle B$, $\angle C$ form an arithmetic sequence. If $\angle A = 23^\circ$, then what is $\angle C$, in degrees? if u can't understand latex then: In triangle ABC, the angles,angle A, angle B, angle C form an arithmetic sequence. If angle A = 23 degrees, then what is angle C, in degrees?

Answer 1

Answer:

$97^0$

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: $T_n=a+(n-1)d$

Where:

a=first term

n=number of term

d=common difference

In this case,

$Angle \:A, a=23^0$

$Angle B, T_2=23+(2-1)d=(23+d)^0\\Angle C, T_3=23+(3-1)d=(23+2d)^0$

The sum of angles in a triangle is 180 degrees. Therefore:

∠A+∠B+∠C=180 degrees

$23^0+(23+d)^0+(23+2d)^0=180\\69^0+3d=180^0\\3d=180^0-69^0\\3d=111^0\\d=37^0$

Therefore:

Angle C,

$(23+2d)^0=(23+2(37))^0=23+74\\C=97^0$