Geometry - Angles at a Point

Solutions

Question 1

a) The square means that the whole angle is a right angle.

A right angle is $90$°

As one of the angles is $60$° then for them to add up to $90$° the other angle must be $30$°

So $x=30$

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b) The square means that the whole angle is a right angle.

A right angle is $90$°

As one of the angles is $75$° then for them to add up to $90$° the other angle must be $15$°

So $x=15$

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c) The square means that the whole angle is a right angle.

A right angle is $90$°

As one of the angles is $45$° then for them to add up to $90$° the other angle must be $45$°

So $x=45$

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d) The square means that the whole angle is a right angle.

A right angle is $90$°

As one of the angles is $30$° then for them to add up to $90$° the other angle must be $70$°

So $x=70$

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e) The square means that the whole angle is a right angle.

A right angle is $90$°

As one of the angles is $50$° then for them to add up to $90$° the other angle must be $40$°

So $x=40$

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f) The square means that the whole angle is a right angle.

A right angle is $90$°

As one of the angles is $8$° then for them to add up to $90$° the other angle must be $82$°

So $x=82$

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g) The square means that the whole angle is a right angle.

A right angle is $90$°

As one of the angles is $52$° then for them to add up to $90$° the other angle must be $38$°

So $x=38$

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h) The square means that the whole angle is a right angle.

A right angle is $90$°

As one of the angles is $27$° then for them to add up to $90$° the other angle must be $63$°

So $x=63$

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Question 2

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