Answer:
[tex]y=28[/tex]
Step-by-step 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:
[tex]34=(x-5)[/tex]
Solving for x:
[tex]x=34+5=39[/tex]
Thus:
[tex]\angle B=x-5 =39-5=34[/tex]
So, since the sum of the interior angles of a triangle is equal to 180:
[tex]\angle A + \angle B + \angle C =180\\\\34+34+4y=180[/tex]
Solving for y:
[tex]4y=180-68\\\\4y=112\\\\y=\frac{112}{4} \\\\y=28[/tex]
And:
[tex]\angle C = 4y= 4*28 =112[/tex]
