Question

The perimeter of the quadrilateral below is 64 units.

Answer 1

Answer:

a = 22

x = 96

y = 144

Step-by-step explanation:

In the given figure

∵ The figure is a quadrilateral

∵ Each two adjacent have the same mark

∴ Every two adjacent sides are equal

∵ The perimeter of the quadrilateral is the sum of its outline sides

∴ The perimeter of the quadrilateral = 10 + 10 + a + a

∴ The perimeter of the quadrilateral = 20 + 2a

∵ The perimeter of the quadrilateral = 64 units

→ Equate the right sides of the perimeter

∴ 20 + 2a = 64

→ Subtract 20 from both sides

∵ 20 -20 + 2a = 64 - 20

∴ 2a = 44

→ Divide both sides by 2 to find a

∴ a = 22

If a line segment joins the vertex of measure y and the vertex of measure 24°, then it will divide the quadrilateral into 2 congruent triangles by the SSS case.

→ Use the result of congruency to find x

∵ The opposite angles of measures x and 96° are equal

∴ x = 96

∵ The sum of the measures of the angle of a quadrilateral is 360°

∴ 96° + y° + 96° + 24° = 360°

→ Add the like terms on the left side

∵ (96 + 96 + 24) + y = 360

∴ 216 + y = 360

→ Subtract 216 from both sides

∵ 216 - 216 + y = 360 - 216

∴ y = 144