Question

In triangle​ ABC, the size of angle B is 3 times the size of angle​ A, and the size of angle C is 12degrees less than 6 times the size of angle A.

Answer 1

Answer:

$A=19.2^o\\B=57.6^o\\C=103.2^o$

Step-by-step explanation:

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

$A+B+C=180$ ----> equation a

$B=3A$ ----> equation b

$C=6A-12$ ----> equation c

Solve the system by substitution

Substitute equation b and equation c in equation a

$A+3A+6A-12=180$

Solve for A

$10A=180+12\\10A=192\\A=19.2^o$

Find the measure of angle B

$B=3(19.2^o)=57.6^o$

Find the measure of angle C

$C=6(19.2)^o-12=103.2^o$