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GEOMETRY, FUR1 2021 VCAA 7 MC

A composite shape is made up of two triangles, as shown in the diagram below.

Two angles, `a^@`  and  `b^@`, are shown on the diagram.
 

Which one of the following statements is always true?

  1. `2a^@ = b^@`
  2. `a^@ = 180^@ - b^@`
  3. `a^@ = 180^@ - 2b^@`
  4. `a^@ = 2b^@ - 180^@`
  5. `2a^@ = 180^@ - b^@`
Show Answers Only

`D`

Show Worked Solution

`text{Base angles of isosceles} \ Δ`

♦♦ Mean mark 32%.

`qquad = 1/2 (180 – a)`
 

`:. 1/2 (180 – a) + b` `= 180`
`180 – a + 2b` `= 360`
`2b – a` `= 180`
`:. a` `= 2b – 180`

 
`=> D`

GEOMETRY, FUR1 2019 VCAA 5 MC

In triangle  `ABC`, the point  `D`  lies on the line  `AC`, as shown in the diagram below.
 


 

The length of the line  `BC`  is equal to the length of the line  `BD`.

Which one of the following statements is true?

  1. The angle  `BAD`  is equal to the angle  `ADB`.
  2. The angle  `ADB`  is equal to the angle  `BDC`.
  3. The sum of the angle  `ACB`  and the angle  `ADB`  is equal to 180°.
  4. The sum of the angle  `ABD`  and the angle  `CBD`  is equal to 180°.
  5. The sum of the angle  `ABC`  and the angle  `ACB`  is equal to the angle  `ADB`.
Show Answers Only

`C`

Show Worked Solution


 

`text(Let)\ \ angle ACB = x`

`angle BDC = x\ \ \ text{(angles opposite equal side in isosceles Δ)}`

`angle ACB + angle ADB` `=x+180-x`  
  `=180`  

`=>  C`

GEOMETRY, FUR1 2015 VCAA 7 MC

A 50 cent coin has 12 sides of equal length.

Two 50 cent coins are balanced next to each other on a table so that they meet along one edge, as shown below.
 

GEO & TRIG, FUR1 2015 VCAA 7 MC
 

The angle, `theta`, is

A.   `12^@`

B.   `30^@`

C.   `36^@`

D.   `60^@`

E.   `72^@` 

Show Answers Only

`D`

Show Worked Solution

GEO & TRIG, FUR1 2015 VCAA 7 MC Answer1

`text(Let)\ \ theta=2x`

`x` `= (360^@)/12\ \ text{(sum of external angles = 360°)}`
  `= 30^@`
`:. theta` `= 60^@`

 
`=> D`