Question

In triangle ABC, if angle A is thirteen less than angle C and angle B is eleven less than four times angle C, find the measure of each angle.

Answer 1

A=21 B=125 C=34

A= C-13
B=4C-11
A+B+C=180 (all angles of a triangle add to 180)
(C-13)+(4C-11)+C=180
6C-24=180
6C=204
C=34
34-13=21=A
4×34-11=125=B

Answer 2

Answer:

$\angle A= 21^\circ\\\angle B =125^\circ\\\angle c = 34^\circ$

Step-by-step explanation:

We are given the following in the question:

A triangle ABC

Let x be the measure of angle C, then according to the question:

$\angle A = x - 13\\\angle B = 4x - 11\\\angle c = x$

Now, according to angle sum property of triangle, the sum of all the three angles of triangle is equal to 180 degrees.

Thus, we can write:

$\angle A + \angle B +\angle C = 180^\circ$

Putting values, we get,

$x - 13 + 4x - 11 + x = 180\\6x - 24 = 180\\6x = 204\\x = 34$

$\angle A = x - 13 = 34-13 = 21^\circ\\\angle B = 4x - 11 = 4(34)-11 = 125^\circ\\\angle c = x = 34^\circ$