Aussie Maths & Science Teachers: Save your time with SmarterEd
Miko is designing a fan using similar triangles.
The edges of the largest and smallest triangles form a right angle.
What is the size of the angle marked `x^@`?
degrees |
`75^@`
Two squares `ABCD` and `EFGH` are shown below.
The area of triangle `FGH` is
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quarter the area of `ABCD` |
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four times the area of `ABCD` |
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one eighth the area of `ABCD` |
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eight times the area of `ABCD` |
`text(quarter the area of)\ ABCD`
`text(Area)\ EFGH` | `= 1/2\ text(Area)\ ABCD` |
`text(Area)\ Delta FGH` | `= 1/2\ text(Area)\ EFGH` |
`:.\ text(Area)\ Delta FGH` | `= 1/4\ text(Area)\ ABCD` |
A regular pentagon, a square and an equilateral triangle meet at a point.
What is the size of the angle `x°`?
`112°` | `110°` | `108°` | `102°` |
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`102°`
`text(Sum of internal angles of hexagon)`
`= (n-2) xx 180`
`= 3 xx 180`
`= 540^@`
`text(Internal angle in hexagon)`
`= 540/5`
`= 108^@`
`:. x` | `= 360-(108 + 90 + 60)` |
`= 102^@` |
`87^@`
Brett drew the shape below using rectangles and straight lines.
What is the value of `x`?
`text(degrees)` |
`164^@`
Igor was designing a shield using 10 identical isosceles triangles, as shown in the diagram below.
How many degrees in the angle marked `x`?
degrees |
`72^@`
`text(Angles at centre of circle)\ = 360/10 = 36^@`
`text{Since triangles are isosceles:}`
`180` | `= 36 + 2x` |
`2x` | `= 180-36` |
`= 144 ` | |
`:. x` | `= 72^@` |
`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)`
`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.)`