Respuesta :
Answer:
[tex]m\angle A=21[/tex]°
[tex]m\angle B=125[/tex]°
[tex]m\angle C=34[/tex]°
Step-by-step explanation:
Let the measure of angle C be [tex]x[/tex]°.
Given:
In triangle ΔABC,
[tex]m\angle A[/tex] is thirteen less than [tex]m\angle C[/tex] and [tex]m\angle B[/tex] is eleven less than four times [tex]m\angle C[/tex]. This gives,
[tex]m\angle A = x-13[/tex]
[tex]m\angle B=4x-11[/tex]
Also, [tex]m\angle C=x[/tex]
Now, for a triangle, the sum of all its interior angles is equal to 180°.
Therefore, [tex]m\angle A + m\angle B + m\angle C=180[/tex]
Plug in all the values and solve for x. This gives,
[tex]x-13+4x-11+x=180\\6x-24=180\\6x=180+24\\6x=204\\x=\frac{204}{6}=34[/tex]
Therefore, measure of angle C is 34°.
Measure of angle A is, [tex]m\angle A=x-13=34-13=21[/tex]°.
Measure of angle B is, [tex]m\angle B=4x-11=4(34)-11=136-11=125[/tex]°.
