Geometry - Angles at a Point
Question 1
Find the value of $x$ in the following diagrams
a)
a
$x=30$
Question ID: 30020010010
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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)
a
$x=15$
Question ID: 30020010020
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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)
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$x=45$
Question ID: 30020010030
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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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$x=70$
Question ID: 30020010040
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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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$x=40$
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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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$x=82$
Question ID: 30020010060
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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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$x=38$
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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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$x=63$
Question ID: 30020010080
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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
Find the value of $y$ in the following diagrams
a)
a
$y=120$
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b)
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$y=134$
Question ID: 30020020020
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$y=90$
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$y=16$
Question ID: 30020020040
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$y=100$
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$y=105$
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$y=69$
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$y=78$
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$y=37$
Question ID: 30020020090
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$y=90$
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$y=107$
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Question 3
Find the value of $z$ in the following diagrams
a)
a
$z=120$
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b)
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$z=80$
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$z=60$
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$z=100$
Question ID: 30020030040
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$z=25$
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$z=15$
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$z=31$
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$z=26$
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$z=43$
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$z=67$
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$z=28$
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$z=37$
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Question 4
Find the value of $q$ in the following diagrams
a)
a
$q=300$
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$q=135$
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$q=270$
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$q=255$
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$q=155$
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$q=40$
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$q=186$
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Question 5
Find the value of $r$ in the following diagrams
a)
a
$r=60$
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$r=100$
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$r=163$
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$r=27$
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$r=90$
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$r=137$
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Question 6
Find the value of the acute angle $\angle AOB$ in the following diagrams, giving reasons
a)
a
$\angle AOB=30$°
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a
$\angle AOB=50$°
Question ID: 30020060020
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$\angle AOB=55$°
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$\angle AOB=78$°
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$\angle AOB=180$°
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$\angle AOB=49$°
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$\angle AOB=74$°
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$\angle AOB=24$°
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Question 7
Find the value of the pronumerals in the following diagrams, giving reasons
a)
a
$x=57$, $y=123$
Question ID: 30020070010
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$a=36$, $b=144$, $c=69$
Question ID: 30020070020
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$m=46$
Question ID: 30020070030
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$h=44$, $j=136$, $k=46$
Question ID: 30020070040
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Question 1
Find the value of $x$ in the following diagrams
a)

b)

c)

d)

e)

f)

g)

h)

Question 2
Find the value of $y$ in the following diagrams
a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

k)

Question 3
Find the value of $z$ in the following diagrams
a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

k)

l)

Question 4
Find the value of $q$ in the following diagrams
a)

b)

c)

d)

e)

f)

g)

Question 5
Find the value of $r$ in the following diagrams
a)

b)

c)

d)

e)

f)

Question 6
Find the value of the acute angle $\angle AOB$ in the following diagrams, giving reasons
a)

b)

c)

d)

e)

f)

g)

h)

Question 7
Find the value of the pronumerals in the following diagrams, giving reasons
a)

b)

c)

d)

Answers
Question 1
a) $x=30$
b) $x=15$
c) $x=45$
d) $x=70$
e) $x=40$
f) $x=82$
g) $x=38$
h) $x=63$
Question 2
a) $y=120$
b) $y=134$
c) $y=90$
d) $y=16$
e) $y=100$
f) $y=105$
g) $y=69$
h) $y=78$
i) $y=37$
j) $y=90$
k) $y=107$
Question 3
a) $z=120$
b) $z=80$
c) $z=60$
d) $z=100$
e) $z=25$
f) $z=15$
g) $z=31$
h) $z=26$
i) $z=43$
j) $z=67$
k) $z=28$
l) $z=37$
Question 4
a) $q=300$
b) $q=135$
c) $q=270$
d) $q=255$
e) $q=155$
f) $q=40$
g) $q=186$
Question 5
a) $r=60$
b) $r=100$
c) $r=163$
d) $r=27$
e) $r=90$
f) $r=137$
Question 6
a) $\angle AOB=30$°
b) $\angle AOB=50$°
c) $\angle AOB=55$°
d) $\angle AOB=78$°
e) $\angle AOB=180$°
f) $\angle AOB=49$°
g) $\angle AOB=74$°
h) $\angle AOB=24$°
Question 7
a) $x=57$, $y=123$
b) $a=36$, $b=144$, $c=69$
c) $m=46$
d) $h=44$, $j=136$, $k=46$
Question 1
Find the value of $x$ in the following diagrams
a)

b)

c)

d)

e)

f)

g)

h)

Question 2
Find the value of $y$ in the following diagrams
a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

k)

Question 3
Find the value of $z$ in the following diagrams
a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

k)

l)

Question 4
Find the value of $q$ in the following diagrams
a)

b)

c)

d)

e)

f)

g)

Question 5
Find the value of $r$ in the following diagrams
a)

b)

c)

d)

e)

f)

Question 6
Find the value of the acute angle $\angle AOB$ in the following diagrams, giving reasons
a)

b)

c)

d)

e)

f)

g)

h)

Question 7
Find the value of the pronumerals in the following diagrams, giving reasons
a)

b)

c)

d)

Answers
Question 1
a) $x=30$
b) $x=15$
c) $x=45$
d) $x=70$
e) $x=40$
f) $x=82$
g) $x=38$
h) $x=63$
Question 2
a) $y=120$
b) $y=134$
c) $y=90$
d) $y=16$
e) $y=100$
f) $y=105$
g) $y=69$
h) $y=78$
i) $y=37$
j) $y=90$
k) $y=107$
Question 3
a) $z=120$
b) $z=80$
c) $z=60$
d) $z=100$
e) $z=25$
f) $z=15$
g) $z=31$
h) $z=26$
i) $z=43$
j) $z=67$
k) $z=28$
l) $z=37$
Question 4
a) $q=300$
b) $q=135$
c) $q=270$
d) $q=255$
e) $q=155$
f) $q=40$
g) $q=186$
Question 5
a) $r=60$
b) $r=100$
c) $r=163$
d) $r=27$
e) $r=90$
f) $r=137$
Question 6
a) $\angle AOB=30$°
b) $\angle AOB=50$°
c) $\angle AOB=55$°
d) $\angle AOB=78$°
e) $\angle AOB=180$°
f) $\angle AOB=49$°
g) $\angle AOB=74$°
h) $\angle AOB=24$°
Question 7
a) $x=57$, $y=123$
b) $a=36$, $b=144$, $c=69$
c) $m=46$
d) $h=44$, $j=136$, $k=46$
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 $x=30$
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 $x=15$
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 $x=45$
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 $x=70$
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 $x=40$
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 $x=82$
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 $x=38$
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 $x=63$
Question 2
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Question 3
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Question 4
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Question 5
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Question 6
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Question 7
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