Answer:
a = 22
x = 96
y = 144
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