Question

15. In AABC if mZA is thirteen less than mzC and mZB is eleven less than four times m

find the measure of each angle.
c ,
mZA =
mZB =
mZC =

Answer 1

`m\angle A=21`°

`m\angle B=125`°

`m\angle C=34`°

Explanation:

Let the measure of angle C be
`x`°.

Given:

In triangle ΔABC,

`m\angle A` is thirteen less than
`m\angle C` and
`m\angle B` is eleven less than four times
`m\angle C`. This gives,

`m\angle A = x-13`

`m\angle B=4x-11`

Also,
`m\angle C=x`

Now, for a triangle, the sum of all its interior angles is equal to 180°.

Therefore,
`m\angle A + m\angle B + m\angle C=180`

Plug in all the values and solve for x. This gives,

`x-13+4x-11+x=180\\6x-24=180\\6x=180+24\\6x=204\\x=(204)/(6)=34`

Therefore, measure of angle C is 34°.

Measure of angle A is,
`m\angle A=x-13=34-13=21`°.

Measure of angle B is,
`m\angle B=4x-11=4(34)-11=136-11=125`°.