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Geometry, NAP-A4-CA13

In the diagram, `ACD` is a straight line.
 

 
What is the size of angle `BCE`?

`45°` `48°` `51°` `87°`
 
 
 
 
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`87^@`

Show Worked Solution

`angleBCA` `= 180 – (81 + 51)qquad(180^@\ text(in triangle))`
  `= 48^@`

 

`:. angleBCE` `= 180 – (48 + 45)qquad(angleACD\ text(is a straight angle))`
  `= 87^@`

Geometry, NAP-D4-CA32

Triangle `PRS`, below, is an isosceles triangle, and `QR = ST`
 

 

 
What are the sizes of the angles marked `x` and `y`?

`x =` 
 
  `­°` `y =` 
 
  `­°`
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`x = 74°\ \ \ y = 106°`

Show Worked Solution

`text(S) text(ince)\ \ Delta PRS\ \ text(is isosceles,)`

`2x + 32` `= 180`
`2x` `= 148`
`:. x` `= 74°`

 
`text(S) text(ince)\ QR = ST`

 `=> Delta PQT\ text(is isosceles)`
 

`text(Let)\ \ /_ PTQ = z°`

`2z + 32` `= 180`
`2z` `= 148`
`z` `= 74°`

 

`:. y` `= 180 – 74\ \ \ text{(180° in a straight line)}`
  `= 106°`

Geometry, NAP-G4-NC18

`AB` is the diameter of a circle, centre `O`.

There are 3 triangles drawn in the lower semi-circle and the angles at the centre are all equal to `x^@`.

The three triangles are best described as:

`text(isosceles)` `text(scalene)` `text(right-angled)` `text(equilateral)`
 
 
 
 
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`text(equilateral)`

Show Worked Solution
`3x` `=180`
`:. x` `=60^@`

 
`AO=OC=OD=OB\ \ text{(radii of circle)}`

`=>\ text{Since angles opposite equal sides of a triangle are}`

`text(equal, all triangle angles can be found to equal 60°.)`

`:.\ text(The three triangles are equilateral.)`