1. This is an isosceles triangle, so 2x = 50º. The sum of all the angles in a triangle must be 180º. These two bits of information are enough to allow you to calculate the value of y.
2. This is an isosceles triangle, with AB = AC. This allows you to find x and hence the size of BC.
3. Same as 2.
4.This is an equilateral triangle, so all the sides are the same length. Equate any two to find the value of x.
5. This is an equilateral triangle, so all the angles are equal to 60º.
1. Since AC = BC.....the two base angles are equal = 50°
And since the sum of three interior angles in a triangle = 180°.......then
50 + 50 + 5y + 10 = 180
110 + 5y = 180 subtract 110 from both sides
5y = 70 divide both sides by 5
y = 14
2. AC = AB .....so
x + 8 = 2x - 1 add 1 to both sides....subtract x from both sides
9 = x
So....BC = 3(9) - 3 = 24
3. Similar to 2
Because angle ACB = angle ABC then AB = AC
2x - 24 = x - 2 add 24 to both sides, subtract x from each side
x = 22 = BC
This is an equilateral triangle....so.....all sides are equal....so we can set any two sides equal and solve for x
4x - 10 = 3x + 2 add 10 to both sides.....subtract 3x from both sides
x = 12