Answer:
![y=28](https://img.qammunity.org/2020/formulas/mathematics/high-school/ga91aympm8d8gi5217isqja6dw8uk8u9wg.png)
Explanation:
This is an isosceles triangle, which are a type of triangles that have a pair of equal sides. Having at least one pair of equal sides allows isosceles triangles to have well-known features. For example, the pair of angles adjacent to the base have the same value because they oppose equal sides within the same triangle.
So, in this case:
![34=(x-5)](https://img.qammunity.org/2020/formulas/mathematics/high-school/7pxy3rtm5ufjjitd4d7biksnm5hcrkz0kn.png)
Solving for x:
![x=34+5=39](https://img.qammunity.org/2020/formulas/mathematics/high-school/uetr7dlzv1rfmrzzjb0maoay5jhyyl3fpf.png)
Thus:
![\angle B=x-5 =39-5=34](https://img.qammunity.org/2020/formulas/mathematics/high-school/54jttg9mqbevr73gkfrmyi915z5c8g2ndv.png)
So, since the sum of the interior angles of a triangle is equal to 180:
![\angle A + \angle B + \angle C =180\\\\34+34+4y=180](https://img.qammunity.org/2020/formulas/mathematics/high-school/tk8fjk37jmp4919bz6mhjhomjbj0sjg38x.png)
Solving for y:
![4y=180-68\\\\4y=112\\\\y=(112)/(4) \\\\y=28](https://img.qammunity.org/2020/formulas/mathematics/high-school/slskoc5934wazetqr4p7e5rlkf0m8etx2a.png)
And:
![\angle C = 4y= 4*28 =112](https://img.qammunity.org/2020/formulas/mathematics/high-school/trpgu48idf6kchd8bpv25cwm6b6i3awces.png)