smc-3165-10-Triangles

Geometry, NAP-A3-CA26

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

`100°`	`110°`	`120°`	`170°`

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`110°`

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`text(From diagram, other interior angle)`

`= 180° – 120°`

`= 60°`

`:. x`	`= 60 + 50`
	`= 110°`	`(text(exterior angle equals the)` `text{sum of interior opposites})`

What is the value of `x°`?

`35°`	`45°`	`55°`	`65°`

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`35°`

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`x`	`= 180 – (55 + 90)`
	`= 35°`

What is the size of the shaded angle?

`105^@`	`110^@`	`120^@`	`125^@`

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`110^@`

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`text(S)text(ince there are 180° in a triangle:)`

An isosceles triangle is drawn below.

What is the size of the angle `angleABC`?

`43.5°`	`45°`	`46.5°`	`60°`

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`43.5^@`

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`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)`

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`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.)`