Answer:
3. (x, y) = (20, 30)
4. (x, y) = (30, 4)
Explanation:
You have equilateral triangles in two different configurations, and you want to find the values marked x and y.
3.
All of the angles marked with an arc are congruent, so all are 60°. The angle marked 80° is an external angle to the top/left triangle. Its value is the sum of the values of the remote interior angles:
80° = 60° +x°
20° = x° . . . . . . . subtract 60°
x = 20
The sides of the equilateral triangle are congruent, so all are length 46. That means the right side is ...
16 +y = 46
y = 30 . . . . . . . subtract 16
(x, y) = (20, 30)
4.
All of the angles marked with an arc are congruent, so all are 60°. The top 60° angle of the equilateral triangle is an external angle to the isosceles triangle at top/right. Its two base angles are the remote interior angles with respect to that 60° exterior angle, so their sum is 60°:
x° +x° = 60°
x = 30
The two marked legs of the isosceles triangle are both 20, which means all sides of the equilateral triangle are length 20.
5y = 20
y = 4 . . . . . . . divide by 5
(x, y) = (30, 4)