Question 1
Given that AB and CD are parallel, find the value of x.
Select the correct answer from the list below:
A: 67^\circ
B: 113^\circ
C: 54^\circ
D: 23^\circ
CORRECT ANSWER: A: 67^\circ
WORKED SOLUTION:
Because angles on a straight line have to add up to 180, we can use this to figure out angle CGF.
\text{CGF}+113=180
\text{CGF}=180-113=67^\circ
Now, because CGF and AFE are corresponding angles, we can say that:
x = AFE = CGF
x=\text{AFE}=67^\circ
Level 6
Question 2
Given that FB and CD are parallel and that AEJ forms an isosceles triangle, find the value of the angle labelled x. State which angle facts you use.
Select the correct answer from the list below:
A: 61^\circ
B: 122^\circ
C: 119^\circ
D: 58^\circ
CORRECT ANSWER: C: 119^\circ
WORKED SOLUTION:
Because vertically opposite angles are equal, we can say that angle \text{AEJ}=58^\circ.
Now, because triangle AEJ is, we know that the angles in the top two corners have to be equal.
And that the angles in this triangle must add up to 180^\circ .
y+y+58^\circ =180^\circ
2y+58^\circ =180^\circ
2y=180^\circ -58^\circ
2y=122^\circ
y=122^\circ \div2
y=61^\circ
Now, because interior angles must add up to 180^\circ we can say that:
z+61^\circ=180^\circ
z =180^\circ -61^\circ
z =119^\circ
Now, because vertically opposite angles are equal, we can say that:
x =119^\circ
Level 6
Question 3
Given that AB and CD are parallel and that JK is perpendicular to AB, find the value of the angle labelled X.
Select the correct answer from the list below:
A: 53^\circ
B: 58^\circ
C: 32^\circ
D: 122^\circ
CORRECT ANSWER: C: 32^\circ
WORKED SOLUTION:
Because JK is perpendicular to AB then it must also be perpendicular to CD, and that it crosses them at 90^\circ.
We can now find the angle LGF by noting that angles on a straight line add up to 180^\circ.
122^\circ+y=180^\circ
y=180^\circ-122^\circ
y=58^\circ
And now, because angles in a triangle add up to 180^\circ, we can find the angle LFG.
58^\circ+90^\circ+z=180^\circ 148^\circ+z=180^\circ z=180^\circ-148^\circ z=32^\circ
Finally, because vertically opposite angles are equal, we must have:
x=z=32^\circ
Level 6
Question 4
Given that AB and CD are parallel, find the value of the angle labelled x.
Select the correct answer from the list below:
A: 49^\circ
B: 131^\circ
C: 56^\circ
D: 112^\circ
CORRECT ANSWER: A: 49^\circ
WORKED SOLUTION:
Because vertically opposite angles are equal we can say that \text{CGF}=49^\circ.
Finally, because corresponding angles are equal, we can say that the angle x=49^\circ
Level 6
Question 5
Given that AB and CD are parallel, find the value of the angle labelled x.
Select the correct answer from the list below:
A: x=101^\circ
B: x=62^\circ
C: x=79^\circ
D: x=39^\circ
CORRECT ANSWER: D: x=39^\circ
WORKED SOLUTION:
Because vertically opposite angles are equal, we can say that \text{GJH}=62^\circ.
Now, because angles in a triangle add up to 180^\circ, we can use that to find angle GHJ.
141^\circ+z=180^\circ
z=180^\circ-141^\circ
Finally, because vertically opposite angles are equal, we can say that x=39^\circ.
Level 6