Answer: For problem 1: x=6, y=13. For problem 2: x=3, y=11
Explanation:
For problem 1:
We are given an equilateral triangle. This is beneficial information, as it tells us not only that all sides are equal in length (hence "equi" and "lateral" or equal sides), but also that all the angles inside the triangle are equal and are 60 degrees.
From this, we can tell that 3x-4 = 14, so x =6. We can also tell that 5y-5 = 60, so y=13
For problem 2:
We are given isosceles triangle JKL, with a vertex of K. An isosceles triangle has only 2 equal sides and equal angles, instead of the 3 equal sides and angles of an equilateral triangle, which is a special isosceles triangle. This means that side JK is equal to side KL in length. Also, angles KJL and KLJ are equal in measure as well.
From this, we can tell that 8x = 13x-15, so x=3. We can also tell that (5y-3) + (5y-3) + 76 = 180, because two angles equal 5y-3, while the vertex angle is 76, and the sum of all angles in a triangle is 180. Thus, y=11