The missing figure is attached
Answer:
∠x = 72° and ∠y = 54°
Step-by-step explanation:
From the first patterns
∵ x is the vertex angle of each isosceles triangle
∵ All the vertices angles of the 5 Δs meet at one point
∵ The sum of the measures of angles around a point is 360°
∴ x + x + x + x + x = 360°
∴ 5 x = 360°
- Divide both sides by 5
∴ x = 72
∴ ∠x = 72°
The sum of the measures of the interior angle of a triangle is 180°
∵ The measure of the vertex angle of each Δ is x
∵ The measures of the base angles of each Δ is y
∴ x + y + y = 180°
- Add like terms in the left hand side
∴ x + 2 y = 180°
∵ x = 72°
∴ 72 + 2 y = 180
- Subtract 72 from both sides
∴ 2 y = 108
- Divide both sides by 2
∴ y = 54
∴ ∠y = 54°
