smc-3189-20-Quadrilaterals

Geometry, NAP-J4-CA15 SA

What is the size of the angle marked `x` in the diagram below?

`text(degrees)`

Show Answers Only

`65°`

Show Worked Solution

`text(Sum of internal angles)\ = 360°`

`:. x`	`= 360 – (102 + 115 + 78)`
	`= 65°`

Bojangles draws an irregular quadrilateral that is shown below.

Which list shows the three angles `a, b, c` in decreasing order of size?

`a, c, b`	`c, b, a`	`a, b, c`	`b, c, a`

Show Answers Only

`b, c ,a`

Show Worked Solution

`b, c, a`

`ABCD` is a rhombus. `AC` is the same length as the rhombus sides.

What is the size of `/_ DCB?`

`90^@`	`100^@`	`110^@`	`120^@`	`130^@`

Show Answers Only

`120^@`

Show Worked Solution

`text(S) text(ince)\ Delta ADC and Delta ABC\ text(are)`

`text(equiangular triangles,)`

`/_ DCA = /_ ACB = 60°`

`:. /_ DCB`	`=60^@ xx 2`
	`=120°`

Eloise makes a sketch of the playground at her school.

What is the size of angle `x°`?

`53^@`	`123^@`	`133^@`	`143^@`

Show Answers Only

`143^@`

Show Worked Solution

`text(Interior angles of a quadrilateral add up to)\ 360^@.`

`:. /_ x`	`= 360-(72 + 88 + 57)`
	`= 143^@`