Here are two different patterns made out of the same five identical isosceles triangles. Without using a protractor, determine the measures of ∠x and ∠y. Explain or show your reasoning.

The missing figure is attached

∠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°

sin3a=12/15

step-by-step explanation:

since one side was multiplied by 3 the other side must also be multiplied by 3.

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this